如题所述
1ï¼å°ºè§ä½å¾ï¼å·²ç¥ä¸æ¤åçé¿è½´ä¸¤ç«¯ç¹åæ¤åä¸å
¶ä»ä»»æä¸ç¹ï¼æ±ä½å
¶å线ã
2ï¼å·²ç¥F1ï¼F2æ¯æ¤å x~2/100+y~2/64=1 ç两个ç¦ç¹ï¼Pæ¯æ¤åä¸çä»»ä¸ç¹ï¼ä¸è§F1PF2=60度ï¼æ±ä¸è§å½¢F1PF2çé¢ç§¯ã
3ï¼å·²ç¥æ¤å x^2/a^2+y^2/b^2=1 åæ¤åä¸ä¸ä¸ªå®ç¹ P(m,n) æ¤åä¸åæå¦ä¸¤ç¹ A,B 满足 PAåç´äºPBãæ±è¯:ç´çº¿ABè¿ä¸å®ç¹ã
4ï¼æ±ä¸å¿å¨åæ åç¹,åæ 轴为对称轴è¿ç¹a(4,1)ä¸ä¸ç´çº¿x+4yâ10=0æä¸åªæä¸ä¸ªå ¬å ±ç¹çæ¤åæ¹ç¨ã
5ï¼è®¾A1ï¼A2åå«ä¸ºæ¤åx^2/a^2+y^2/b^2ï¼1å¨xè½´ä¸ç两个端ç¹ãP为æ¤åä¸ä¸å¨ç¹ï¼F为æ¤åçå³ç¦ç¹ãç»åºæ¤åçå³å线ï¼åå«è¿æ¥A1-Pï¼A2-Pï¼å»¶é¿åä¸å线çç¦ç¹åå«ä¸ºMNãæ±è§MFNç度æ°ã
6ï¼æ¤åEçä¸å¿å¨åç¹O,ç¦ç¹å¨xè½´ä¸,é«å¿çe=æ ¹å·ä¸(2/3),è¿ç¹C(-1,0)çç´çº¿L交æ¤åäºA,B两ç¹,ä¸CAåé=λBCåé (λâ¥2).
(1).è¥Î»ä¸ºå¸¸æ°,ç´çº¿Lçæç为K(Kä¸ä¸º0),ååºâ³OABçé¢ç§¯Så ³äºKç表达è¯f(K)
(2).è¥Î»ä¸ºå¸¸æ°,å½Sæ大æ¶,æ±æ¤åEçæ¹ç¨
7ï¼å¨æ¤åx~2/25+y~2/9=1ä¸ä¸ç¹p,使å®å°å·¦ç¦ç¹çè·ç¦»æ¯å®å°å³ç¦ç¹è·ç¦»ç2å.
8ï¼å¨æ¤å x~2/45 + y~2/20 ä¸æ±ä¸ç¹ï¼ä½¿å®ä¸ä¸¤ç¦ç¹çè¿çº¿äºç¸åç´ã
9ï¼è¿æ¤åX~2/a~2+Y~2/b~2=1[0<b<a]ä¸å¿çç´çº¿ä¸æ¤å交äºA,B两ç¹,å³ç¦ç¹ä¸ºF(c,0),åä¸è§å½¢ABF2çæ大é¢ç§¯æ¯ï¼ ï¼ã
A ab B ac C bc D b~2
10ï¼ç´çº¿y=x-1åæ¤åx^2/m+y^2/(m-1)=1(m大äº1ï¼äº¤äºAãBï¼ä»¥AB为ç´å¾çåè¿æ¤åçç¦ç¹Fï¼æ±å®æ°mçå¼ã
11ï¼ä¸ä¸ªé¿è½´ä¸º2a,ç轴为2bçæ¤åï¼å¨ç¬¬ä¸è±¡éå æ»å¨ï¼å¹¶å§ç»ä¸Xè½´ï¼Yè½´é½ç¸åãæ±è¯¥æ¤åä¸å¿Cç轨迹æ¹ç¨ã
12ï¼å·²ç¥ä¸¤å®åC1:ï¼X-2ï¼~2+Y~2=1ï¼C2ï¼ï¼X+2ï¼~2+Y~2=81ï¼ä¸å¨åCä¸C1å¤åï¼ä¸åC2å åï¼æ±å¨ååå¿ç轨迹æ¹ç¨ã
13ï¼ä¸è§å½¢ABCç两个顶ç¹A.Bçåæ åå«æ¯(-5,0),(5,0),è¾¹AC,BCæå¨ç´çº¿çæçä¹ç§¯ä¸º-1/2,æ±é¡¶ç¹Cç轨迹æ¹ç¨.
14ï¼å·²ç¥æ¤åçç¦ç¹å¨æ¨ªè½´ä¸ï¼è¿ç¦ç¹Fçç´çº¿äº¤æ¤åäºPQ两ç¹ï¼ä¸æ»¡è¶³OPâ¥OQï¼æ±æ¤å离å¿ççåå¼èå´
15ï¼æ¤åX~2/a~2+Y~2/b~2=1(a>b>0)ååX~2+Y~2=(b/2 + C)~2,交äºå个ä¸åç¹,åæ¤åç离å¿ççåå¼èå´?
16ï¼è®¾æ¤åä¸åæ²çº¿æå ±åçç¦ç¹F1ï¼ï¼4ï¼0ï¼åF2ï¼4ï¼0ï¼ï¼å¹¶ä¸æ¤åçé¿è½´é¿æ¯åæ²çº¿å®è½´é¿ç2åï¼è¯æ±æ¤åä¸åæ²çº¿äº¤ç¹ç轨迹æ¹ç¨ã
17ï¼è¥æ¤åX~2/4+Y~2/3=1ä¸æä¸åçç¹PãQå ³äºç´çº¿y=4x+m对称ï¼æ±mçåå¼èå´ï¼
18ï¼æ¤å X^2/A^2+Y^2/B^2=1 (A>B>1)ä¸ä¸¤ç¹M,N.MN=L (å®é¿)ï¼L>2*B^2/A. æ±MNä¸ç¹æ¨ªåæ çæ大å¼.ç¨A,B,L表示.
19ï¼æ¤åx~2/9+y~2/4=1, ç¦ç¹ä¸ºF1,F2,P为æ¤åä¸ä¸å¨ç¹,åä¸è§PF1F2é¢ç§¯çæ大å¼æ¯å¤å°?
20ï¼æ¤åçé¢ç§¯å ¬å¼æ¯ä»ä¹ï¼
21ï¼è¿æ¤åx~2/a~2+y~2/b~2=1(a>b>0)çå³ç¦ç¹Fçä»»æç´çº¿äº¤yè½´äºPç¹ ï¼äº¤æ¤åäºM,N æ±è¯: PM/MF+PN/NF为å®å¼ã
22ï¼ä¸æç为3/4çç´çº¿è¿ä¸ä¸å¿å¨åç¹çæ¤åå·¦ç¦ç¹ï¼ä¸ä¸æ¤åçäºäº¤ç¹ä¸ï¼æä¸äº¤ç¹çºµåæ 为3ï¼å·²ç¥æ¤åå³ç¦ç¹å°ç´çº¿çè·ç¦»ä¸º12/5ï¼æ±æ¤åçæ åæ¹ç¨ï¼
23ï¼è¿åx~2+y~2=4å ä¸ç¹a(1,0)ååç弦,æ±è¿äºå¼¦çä¸ç¹mç轨迹æ¹ç¨.
24ï¼æ¤å:X^2/a^2+y^2/b^2=1(a>b>0)çå·¦ï¼å³ç¦ç¹åå«æ¯F1,F2 å³ç¦ç¹ç顶ç¹ä¸ºA.M为æ¤åãC1ä¸ä»»æä¸ç¹ï¼ä¸MF1*MF2çæå°å¼æ¯3/4a^2
ï¼1ï¼æ±åæ²çº¿C2
ï¼2ï¼ä»¥æ¤åçC1çç¦ç¹ä¸ºé¡¶ç¹ï¼é¡¶ç¹ä¸ºç¦ç¹ï¼å¨ç¬¬ä¸è±¡éå ä»»ååæ²çº¿C2ä¸ä¸ç¹P,è¯é®æ¯å¦åå¨å¸¸æ°Q(Q>0).使å¾è§PAF1=Qåçè§PF1Aææç«ï¼
25ï¼è¿æ¤åå·¦ç¦ç¹Fä¸å¾æè§ä¸º3/Ïçç´çº¿äº¤æ¤åäºA,B两ç¹ï¼è¥|FA|=2|FB|ï¼åæ¤åç离å¿çæ¯ï¼ ï¼ã
26ï¼é®é¢ï¼ç¥éæ¤åçé¿è½´åçè½´ï¼æä¹æ±ç¦è·ï¼
27ï¼å·²ç¥æ¤åC x²/a²+y²/b²=1 设Aï¼X1ï¼Y1ï¼ï¼Bï¼X2ï¼Y2ï¼ï¼X1ä¸çäºX2ä¸Y1ä¸çäºY2ï¼ä¸ºæ¤åä¸ä¸¤ç¹ï¼Aï¼B两ç¹ç对称轴lå¨Xè½´ãYè½´ä¸çæªè·åå«ä¸ºmãn.æ±è¯ï¼ï¼a²-m²)/b²+(b²-n²)/a²>2
28ï¼æ¤åçæ¹ç¨æ¯x~2/4b~2+y~2/b~2=1 ï¼æ¤åä¸æä¸ç¹På°å³ç¦ç¹çè·ç¦»ä¸ºbï¼æ±På°å·¦å线çè·ç¦»ã
29ï¼å·²ç¥åCä¸åC1ï¼x~2+ (y-4)~2= 64å åï¼ä¸åC2ï¼x~2+ (y+4)~2= 4å¤åãæ±Cçåå¿è½¨è¿¹ã
30ï¼x^2/25+y^2/9=1 ï¼ç¹A(x1,y1),B(4,y2),C(x3,y3)å¨æ¤åä¸ï¼ F为å³ç¦ç¹ ï¼AF+CF=2BF ï¼æ±ACä¸ç¹è½¨è¿¹ã
31ï¼æ¤å两ç¦ç¹åä¸å¿å°ä¸¤å线çè·ç¦»åçåï¼åä¸ç¦ç¹ä¸ç轴两端ç¹è¿çº¿é´ç夹è§ä¸ºï¼ ï¼ã
32ï¼P为æ¤åä¸ä¸ç¹ï¼F₁ãF₂ 为æ¤åç¦ç¹ï¼Xè½´ä¸ï¼ï¼AãB为æ¤åå·¦ãå³é¡¶ç¹ï¼å½Pç¹ä¸ºæ¤åä¸é¡¶ç¹æä¸é¡¶ç¹æ¶ï¼è§F₁PF₂ãè§APB ææ大å¼ï¼
[S(F1PF2)=b^2*tan(è§F1PF2/2)]
33ï¼Pï¼xï¼yï¼ä¸ºæ¤åX~2ï¼3ï¼y~2ï¼1ä¸çç¹ï¼åPç¹å°ç´çº¿Xï¼Yï¼2çæ大è·ç¦»æ¯å¤å°ï¼
34ï¼è®¾æ¤åx~2/a~2+y~2/b~2=1(a>b>0)çå·¦å³ç¦ç¹åå«ä¸ºF1,F2,æ¤åä¸åå¨ç¹p,使è§F1pF2为éè§,æ±ç¦»å¿ççèå´ã
35ï¼ä¸é¢äººé å°çå«æçè¿è¡è½¨éå°ä»¥å°ççä¸å¿ä¸ºä¸ä¸ªç¦ç¹çæ¤åï¼è¿å°ç¹Aè·å°é¢439KMï¼è¿å°ç¹Bè·å°é¢2384KMï¼å°çåå¾çº¦ä¸º6371KM ï¼æ±å«æç轨éæ¹ç¨ã
36ï¼è®¾Aï¼X1ï¼Y1ï¼ä¸ºæ¤åX^2+2y^2=2ä¸çä»»ä¸ç¹ï¼è¿Aä½ä¸æ¡æç为-X1/2Y1çç´çº¿Lï¼å设d为åç¹å°Lçè·ç¦»ï¼r1ï¼r2åå«ä¸ºç¹å°ä¸¤ç¦è·çè·ç¦»ï¼æ±è¯æ ¹å·r1*æ ¹å·r2*d为å®å¼ã
37ï¼å¨ä¸è§å½¢ABCä¸ï¼Bï¼4ï¼0ï¼ï¼Cï¼-4ï¼0ï¼ï¼ç¹Aè¿å¨æ¶æ»¡è¶³sinA-sinB=1/2*sinAï¼æ±Aç¹ç轨迹ã [è¿æ¯ä¸ä¸ªå»é¤ä¸¤é¿è½´ç«¯ç¹çæ¤å]
38ï¼å·²ç¥ç¹Påæ æ¯ï¼-1ï¼-3ï¼ï¼F为æ¤åX^2/16+Y^2/12=1çå³ç¦ç¹ï¼ç¹Qå¨æ¤åä¸ç§»å¨ï¼å½|QF|+0.5|PQ|åæå°å¼æ¶ï¼æ±ç¹Qåæ ï¼å¹¶æ±å ¶æå°å¼ã
39ï¼å·²ç¥æ¤åX2/a2+Y2/b2=1(a>b>0)åç¹B(0,b)ï¼ Pæ¯æ¤åä¸å¨ç¹ï¼ æ±BPé¿åº¦çæ大å¼ã[è¦å类讨论
40ï¼è¿æ¤åå³ç¦ç¹Fä½å¾æè§ä¸º120°çç´çº¿äº¤æ¤åäºAãB两ç¹ï¼è¥|FA|=2|FB|åæ¤åç离å¿çæ¯ï¼ ï¼ã
41ï¼æ¤åæ¹ç¨x2ï¼4+y2ï¼3ï¼1ï¼å³ç¦ç¹F(1,0),ç¹P(1,1),Mç¹å¨æ¤åä¸ï¼æ±MP+2MFçæå°å¼ã
42ï¼A,B两个æ¹åå¸åº,ååæ¹åä»·ç¸å,ä½å¨æå°åºçå± æ°ä»ä¸¤å°è¿åååæ¶,æ¯åä½è·ç¦»çè¿è´¹ä¸å,Aå°è¿è´¹æ¯Bå°ç两å,å·²ç¥A,B两å°ç¸è·10å ¬é,é®:å± æ°å¦ä½éæ©è¿è´§å°ç¹,æè½ä½¿è¿è´¹æ便å®.
43ï¼è®¾F1,F2æ¯æ¤å(X^2)/4+(y^2)/3=1çå·¦å³ç¦ç¹,Aæ¯æ¤åä¸å¨ç¹,è¿F1ä½è§F1AF2çå¤è§çå¹³å线çå线,设å足为P,æ±Pç轨迹
44ï¼æ±ä»¥åç¹ä¸ºå³ç¦ç¹,ç´çº¿x=1为å³å线çå¨æ¤åç轴端ç¹ç轨迹æ¹ç¨ã
45ï¼è®¾M,N为æ¤åx^2/9+y^2/4=1ç两ç¦ç¹,Pæ¯æ¤åä¸çä¸ç¹,å·²ç¥P,M,Næ¯ä¸ä¸ªç´è§ä¸è§å½¢çä¸ä¸ªé¡¶ç¹ä¸|PM|>|PN|.æ±|PM|/|PN|çå¼.
46ã设å¨åPè¿å®ç¹A(-3,0),并ä¸å¨å®åB:(x-3)2+y2=64çå é¨ä¸å ¶å å,æ±å¨åçåå¿Pç轨迹æ¹ç¨?
47ï¼å·²ç¥æ¤åx^2/6+y^2/2=1,对åºäºç¦ç¹F(c,0)çå线lä¸xè½´ç¸äº¤äºç¹A,è¿Açç´çº¿ä¸æ¤å交äºP,Q两ç¹,è¥PQç´çº¿çæç为[æ ¹3]/3,æ±ä¸è§å½¢FPQçé¢ç§¯ã
48ï¼è¿æ¤åçå·¦ç¦ç¹ä½åç´äºXè½´ç´çº¿äº¤æ¤åä¸Mï¼ä¸æ¤åçä¸é¡¶ç¹ä¸å³é¡¶ç¹è¿çº¿å¹³è¡ä¸MOï¼æ±æ¤åç离å¿çã
49ï¼å·²ç¥æ¤åï¼X~2/4+Y~2=1ï¼æç´çº¿Lï¼X=Tï¼T为大äº2çå®å¼ï¼ä¸X轴交äºç¹Tï¼P为Lä¸å¼äºTçä»»æä¸ç¹ï¼A1,A2æ¯æ¤åå·¦å³ç«¯ç¹ï¼ç´çº¿PA1ï¼PA2åå«ä¸æ¤åC交äºM.Nï¼é®ç´çº¿MNæ¯å¦ç»è¿Xè½´ä¸çä¸ä¸ªå®ç¹ï¼å¹¶è¯æä½ çç»è®ºã
[æ¤å®ç¹å¨é¿è½´å»¶é¿çº¿ä¸.]
å¦æä½ äºè§£æç¹æ线åå°å½±æ¹æ³çè¯,å¯ä»¥èèå ä½çè¯æ³.
ä¸è¬å:ç´çº¿Låç´äºæ¤åçé¿è½´....(åé¢çååé¢ç¸å)..
é¦å è¯æ对åçæ å½¢æç«,è¿éè¦æç¹æ线çç论.
ç¶åææ´ä¸ªå¾æ²¿ç´å¾æ¹åæ伸,æ¤ååè¿ç¨ä¸,ç¹çº¿çç»åæ§ä¿æä¸åã
50ï¼è®¾æ¤åä¸åæ²çº¿æå ±åç¦ç¹f(-4,0)åF(4,0)ï¼å¹¶ä¸æ¤åçé¿è½´é¿æ¯åæ²çº¿å®è½´é¿çäºåï¼è¯æ±æ¤åä¸åæ²çº¿äº¤ç¹ç轨迹æ¹ç¨ã
51ï¼å·²ç¥æ¤åCçä¸å¿å¨åç¹ï¼ç¦ç¹å¨è½´ä¸ï¼ç¦»å¿çE=1/2ï¼ä¸ç»è¿ç¹Mï¼-1ï¼3/2ï¼ãï¼1ï¼æ±æ¤åCçæ¹ç¨ï¼ï¼2ï¼è¥æ¤åCä¸æä¸åç两ç¹Pï¼Qå ³äºç´çº¿Y=4X+M对称ï¼æ±Mçåå¼èå´ã
52ï¼æ¤åæ¹ç¨ä¸º x~2/25 + y~2/16 = 1ï¼ æ¤åå ä¸å®ç¹Aï¼2ï¼1ï¼ ï¼å¨æ¤åä¸æ±ä¸ç¹Bï¼æ¯çº¿æ®µABçè·ç¦»æ大ã[å°é¾]
53ï¼xy=1ç离å¿ç为ä»ä¹çäºæ ¹å·2
54ï¼å·²ç¥æ¤åçé¿åè½´æ¯çåè½´ç3åï¼è¿å·¦ç¦ç¹å¾æè§ä¸º30度ç弦é¿ä¸º2ï¼åæ¤æ¤åçæ åæ¹ç¨ä¸ºï¼ ï¼ã
55ï¼å¨æ¤åx^2/a^2+y^2/b^2=1ä¸ï¼å½ä¸æ¡ç´çº¿ç©¿è¿å®æ两交ç¹Aï¼ B ï¼ è¿åå¿ O åæ¤åå 弦ABçä¸ç¹C ï¼ é£ä¹ç´çº¿ABæçä¸OCæçä¹ç§¯çäº âb~2/a~2ã
56ï¼å¨æ¤åx^2/a^2+y^2/b^2=1å ä½ä¸ä¸ªå æ¥ç©å½¢ï¼è¯é®é¿å®½åæ¯å¤å°æ¶ï¼é¢ç§¯æ大ï¼é¢ç§¯å¼æ¯å¤å°ï¼
57ï¼è®¾Aï¼Bæ¯æ¤å3x^2+y^2=pä¸ä¸¤ç¹ï¼ç¹Nï¼1ï¼3ï¼æ¯çº¿æ®µABçä¸ç¹ï¼çº¿æ®µABçåç´å¹³å线ä¸æ¤å交äºCD两ç¹ï¼è¯ç¡®å®pçèå´ï¼ä½¿ABCDåç¹å ±åã
58ï¼æ¤åçç¦ç¹F1,F2,è¿ç¦ç¹ä½ç´çº¿ä¸æ¤åç¸äº¤ï¼è¢«æ¤åæªå¾çæç线段MN为3/5,ä¸è§å½¢MF2Nçå¨é¿ä¸º20ï¼åæ¤åç离å¿çæ¯ï¼ ï¼ã
59ï¼æ¤å X~2/4+y~2/2=1ä¸.è¿ç¹P(1ï¼1)ç弦被Pç¹å¹³å,æ±æ¤å¼¦æå¨çç´çº¿æ¹ç¨å弦é¿ã
60ï¼å·²ç¥ç¹Aï¼4ï¼0ï¼åBï¼2ï¼2ï¼ï¼ç¹Mæ¯æ¤åX^2/25+Y^2/9=1ä¸çå¨ç¹ï¼åMA+MBçæ大å¼æ¯ï¼ ï¼ã
61ï¼æå¨é¢ä¹ é«äºä¸ç解æå ä½ï¼å¨æ¤åé书ä¸åªè®²äºæ²¡ææ转è¿çæ¤åæ¹ç¨ï¼æçå°ä¸é¢ æ¯å¦ä¸¤ä¸ªç¦ç¹æ¯ï¼1ï¼1ï¼åï¼-1ï¼-1ï¼ ä»»ææ¤åä¸ä¸ç¹å°ä¸¤ç¦ç¹è·ç¦»å为4ï¼æ±è¿ä¸ªæ¤åçæ¹ç¨ï¼æä¹åï¼
62ï¼ç¹Må°ç¹A(-4,0)ä¸ç¹B(4,0)çè·ç¦»çå为12,æ±ç¹Mç轨迹æ¹ç¨ã
63ï¼ç»è¿ç¹Pï¼ï¼3ï¼2ï¼ä¸ä¸ï¼X~2ï¼9ï¼Y~2ï¼4ï¼1æç¸åçç¦ç¹çæ¤åæ¹ç¨ï¼
64ï¼æ¤åx^2/100+y^2/64=1çç¦ç¹ä¸ºaï¼bï¼æ¤åä¸çç¹p满足è§apbï¼60度ï¼åé¢ç§¯apbæ¯å¤å°ï¼
65ï¼æ±ç»è¿ç¹M(1,2),以y轴为å线ï¼ç¦»å¿ç为0.5çæ¤åçå·¦å®ç¹ç轨迹æ¹ç¨ã
66ãæ¤å X~2/4+Y`2=1 ä¸Xè½´ç交ç¹ä¸ºA(2,0) B(-2,0),ä¸Yè½´å¹³è¡çç´çº¿äº¤è¯¥æ¤åäºP,Q两ç¹ï¼æ±APåBQ交ç¹mçæ²çº¿æ¹ç¨ã
67ãå·²ç¥ç´çº¿Y=X+Måæ²çº¿ X~2+2Y~2+4Y-1=0,交äºA,BãPæ¯è¿æ¡ç´çº¿ä¸çä¸ç¹ï¼ä¸âPAâ*âPBâ=2 ï¼æ±å½Mååæ¶ç¹Pç轨迹æ¹ç¨ï¼å¹¶è¯´æå½¢ç¶ã
68ãæ±ç»è¿åç¹ï¼ä»¥F(2,0)为å®çä¸ä¸ªç¦ç¹ï¼é¿è½´2a=bçæ¤åä¸å¿ç轨迹æ¹ç¨ã
69ãå·²ç¥ä¸¤åC1:X~2+Y~2+6Y=0,åC2:X~2+Y~2-6X-40=0ãæ±ä¸ä¸åå åï¼ä¸ä¸åå¤åçå¨ååå¿ç轨迹æ¹ç¨ã
70ãå·²ç¥ä¸¤åC1:(X-4)~2+Y~2=169 ï¼C2:ï¼X+4ï¼~2+Y~2=9ï¼å¨åå¨C1å é¨ä¸ååC1ç¸å åï¼ä¸C2ç¸å¤åï¼æ±å¨ååå¿ç轨迹æ¹ç¨ã
71ãæ¤åX~2/a~2+y~2/b~2=1 å æ¥ä¸è§å½¢ABCï¼å®çä¸è¾¹BCä¸é¿è½´éåï¼Aå¨æ¤åä¸è¿å¨ï¼è¯æ±ä¸è§å½¢ABCä¸å¿ç轨迹ã
72ï¼æ¤å两ç¦ç¹åä¸å¿å°ä¸¤å线é´çè·ç¦»åçåï¼åä¸ç¦ç¹ä¸ç轴两端ç¹è¿æ¥ç夹è§æ¯å¤å°ï¼
73ãæ¤åX~2/4 + Y~2/3 =1,ç¡®å®Mçå±æèå´ä¼¼ç对äºç´çº¿Y=4MX+Mæ¤åä¸æä¸åç两ç¹å ³äºç´çº¿å¯¹ç§°.
74ã设X~2/A~2+ Y~2/B~2 =1(A>B>0)ä¸ç´çº¿X+Y-1=0交äºPQ,ä¸PQåç´OQ,æ±è¯1/A~2+1/B~2为å®å¼.è¥E(离å¿ç)å±äº[æ ¹3/3,æ ¹2/2],æ±é¿è½´çåå¼èå´ ã
75ï¼æ¤å x^2/25 + y^2/16 = 1 å æ两ç¹: M(2,2) N(3,0) ï¼Pæ¯æ¤åä¸ä»»æä¸ç¹ æ±|PM|+|PN|çæå°å¼ã
76ï¼è®¾æ¤åæ¹ç¨ä¸ºX~2/A~2+ Y~2/B~2 =1(A>B>0)ï¼çè½´çä¸ä¸ªé¡¶ç¹Bä¸ä¸¤ç¦ç¹F1ï¼F2ç»æçä¸è§å½¢çå¨é¿ä¸º4+2æ ¹3ï¼ä¸è§F1BF2为120度ï¼æ±æ¤åæ¹ç¨ã
77ãæ¤åçç¦è·æ¯é¿è½´é¿ï¼çè½´é¿ççæ¯ä¸é¡¹ï¼åæ¤åç离å¿çæ¯å¤å°ï¼
78ã设P为æ¤åæ åæ¹ç¨ä¸ä»»ä¸ç¹ï¼F1ï¼F2åå«ä¸ºå·¦ï¼å³ç¦ç¹ï¼æ±PF1çç»å¯¹å¼ä¸PF2çç»å¯¹å¼çæ大å¼åæå°å¼ã
79ï¼å¨æ¤åä¸ä»¥ç¦ç¹F1F2为ç´å¾ä¸¤ç«¯ç¹çåï¼æ°å¥½è¿çè½´ç两顶ç¹ï¼åæ¤æ¤åç离å¿ççäºå¤å°ï¼
80ï¼Pæ¯æ¤åX~2+2Y~2=16ä¸çå¨ç¹ï¼Fæ¯ä¸ä¸ªç¦ç¹ï¼åPFçæå°å¼æ¯å¤å°ï¼
81ï¼å¨ååå®åM:x~2+y~2-4y-32=0å å,ä¸è¿å®ç¹A(0,-2),æ±å¨ååå¿Pç轨迹ã
82ï¼è¿æ¤å2X~2+Y~2=2çä¸ç¦ç¹çç´çº¿L交æ¤åäºAï¼B两ç¹ï¼æ±ä¸è§å½¢AOBï¼O为åç¹ï¼çé¢ç§¯æ大å¼ï¼
83ï¼å¨Y=Xçå¾è±¡ä¸ï¼ æ¾ä¸ç¹P ï¼Pä¸A(2.0)åä¸(-2.0)çè·ç¦»ä¹å为8 ï¼æ±Påæ ã
84ï¼å¨æ¤åä¸æ±ä¸ç¹ä½¿å®å°æ¤åå¤ç两å®ç¹è·ç¦»åçæ大å¼ãæå°å¼ã
85ï¼è¥æ¤åé¿è½´,çè½´,ç¦è·çé¿åº¦ä¹åçäº8,åé¿åè½´çåå¼èå´æ¯_____,å½é¿åè½´åå¾æå°å¼æ¶,æ¤åç离å¿ççäº_____.
86ï¼è¿æ¤åC:X~2/4+Y~2=1çå³ç¦ç¹,ä½ä¸ç´çº¿l交æ¤åCäºM,Nå°å³å线X=4/æ ¹3çè·ç¦»ä¹åä¸ºæ ¹3,æ±ç´çº¿læ¹ç¨.
87ï¼å·²ç¥A(4,0),B(2,2)æ¯æ¤åx~2/25+y~2/9=1å çç¹,Mæ¯æ¤åä¸çå¨ç¹.æ±|MA|+|MB|çæ大å¼ä¸æå°å¼.
88ï¼å·²ç¥æ¤åä¸ç¹ä¸ºåç¹, ç¦ç¹å¨æ¨ªè½´ä¸ï¼ç¦»å¿çä¸ºæ ¹3/2ï¼ä¸x+y+1=0交äºPãQ,å½OPåç´OQæ¶ï¼æ±æ¤åæ¹ç¨ã
89ï¼æ±ååæ²çº¿X~2-Y~2=8æå ±åç¦ç¹ä¸ç»è¿ç¹Pï¼4ï¼6ï¼çæ¤åçæ¹ç¨ã
90ï¼ä»¥ï¼2ï¼0ï¼ä¸ºç¦ç¹ï¼y轴为å线çæ¤åæå 个ï¼
91ï¼æ¤åX~2/A~2+Y~2/B~2=1ï¼ï¼A>B>0ï¼ç两ç¦ç¹ä¸ºF1ãF2ï¼æç为Kçç´çº¿è¿å³ç¦ç¹F2ï¼ä¸æ¤å交äºAãBï¼ä¸Y轴交äºCï¼B为F2ä¸ç¹ï¼è¥Kçç»å¯¹å¼å°äºçäº2[æ ¹5]/5ï¼æ±æ¤å离å¿çèå´ã
92ãå·²ç¥æ¤åç两个ç¦ç¹åå«æ¯F1(-2æ ¹å·2,0),F2(2æ ¹å·2)é¿è½´é¿ä¸º6,ç´çº¿X-Y+2=0 ä¸æ¤åç¸äº¤äºA,B两ç¹ãæ±: (1)æ¤åçæ åæ¹ç¨ (2)线段ABçé¿åº¦
93ï¼ä¸æ¤åä¸ä¸¤ç¹p,q, opåç´oq,å1/OPæ¹+ 1/OQæ¹æ¯å®å¼ã
94ï¼çº¿æ®µABå®é¿ï¼Cæ¯ABä¸çä¸ä¸ªå®ç¹ï¼ç¸å¯¹ABåºå®ï¼ï¼AB两端ç¹åå«å¨ä¸¤å®ç´çº¿ä¸è¿å¨ï¼æ±Cçè½¨è¿¹ï¼ [æ¯ä¸ªæ¤å]
95ï¼æ¤åå æ¥æ£æ¹å½¢çé¢ç§¯æä¹æ±?
96ï¼æ¤åx^2/a^2+y^2/b^2=1(a>b>0)çå·¦å³ç¦ç¹åå«ä¸ºF1åF2ï¼A1(-a,0)ï¼A2(a,0)ï¼B(0,b)ï¼Pæ¯æ¤åä¸ä¸ç¹ï¼è¥F2å°ç´çº¿ABçè·ç¦»ä¸ºb/æ ¹å·7ï¼æ±æ¤åç离å¿çã
97ï¼æ±ä»¥ï¼Â±4ï¼0ï¼åï¼0ï¼Â±3ï¼ä¸ºé¡¶ç¹çæ¤åçæ åæ¹ç¨ã
98ï¼pæ¯æ¤å(aï¼bï¼0)ä¸å¼äºé¿è½´ç«¯ç¹çä»»ä¸ç¹ï¼F1ãF2æ¯æ¤åç两个ç¦ç¹ï¼è¥â PF1F2=α,â PF2F1=βï¼æ±è¯ï¼
æ¤åç离å¿çe=cos0.5ï¼Î±+βï¼/cos0.5ï¼Î±ï¼Î²ï¼
99ï¼ç¹Aï¼Båå«æ¯æ¤åXï¼¾ï¼36+Yï¼¾ï¼20ï¼1é¿è½´çå·¦ï¼å³ï¼ç¹Fæ¯æ¤åçå³ç¦ç¹ï¼ç¹På¨æ¤åä¸ï¼ä¸ä½äºXè½´ä¸æ¹ï¼PAâ¥PB
ï¼1ï¼æ±Pç¹çåæ ï¼
ï¼2ï¼è®¾Mæ¯æ¤åé¿è½´ABä¸çä¸ç¹ï¼Må°ç´çº¿APçè·ç¦»çäºï¼MBï¼ï¼æ±æ¤åä¸çç¹å°ç¹Mçè·ç¦»dçæå°å¼ï¼
100ï¼å·²ç¥ç¹Aï¼ï¼2ï¼0ï¼ï¼Bï¼3ï¼0ï¼ï¼å¨ç¹Pï¼x,yï¼æ»¡è¶³åéçç¹ç§¯PA*PBï¼x~2ï¼åç¹ç轨迹æ¯AåBæ¤åCåæ²çº¿Dæç©çº¿ã
101ï¼å·²ç¥M为æ¤åä¸ä¸ç¹ï¼F1F2æ¯ä¸¤ç¦ç¹ï¼ä¸â MF1F2=2αï¼â MF2F1=α(αâ 0)ï¼åæ¤åç离å¿çæ¯( )ã
102ï¼P为æ¤å x^2/25+y^/16=1ä¸ä¸ç¹ï¼F1ãF2为左å³ç¦ç¹ãï¼1ï¼è¥PF1çä¸ç¹ä¸ºMï¼æ±è¯â£MOâ£=5â1/2â£PF1â£ãï¼2ï¼è¥â F1PF2=60°ï¼æ±â£PF1â£*â£PF2â£çå¼ãï¼3ï¼æ±â£PF1â£*â£PF2â£çæå¼
103ï¼ææ¤åX^2/6+Y^2/2=1,ç¹N(3,0),è¿Nçç´çº¿ä¸åä½åX^2+Y^2=1æ¤å交äºP,Q,R,S,ä¸|PQ|=|RS|,æ±æ¯å¦åå¨,åå¨å³æ±åºè¯¥ç´çº¿ã
104ï¼è®¾ç´çº¿Y=2x+1ä¸æ¤åX~2/4+Y~2=1ç¸äº¤äºAB两ç¹ï¼æ±AB两ç¹Må°åæ åç¹çè·ç¦»ã
105ï¼å·²ç¥æ¤åx2+2y2=98åç¹p(0,5),æ±æ¤åä¸çç¹å°pçè·ç¦»çæ大å¼åæå°å¼
106ï¼å·²ç¥æ¤åx^2/a^2+y^2/b^2=1(a>b>0)ç离å¿çæ¯[æ ¹6]/3ï¼Fæ¯å ¶å·¦ç¦ç¹ï¼è¥ç´çº¿x-æ ¹6=0ä¸æ¤å交ä¸AB两ç¹ï¼ä¸åéFA*åéFB=-1,æ±è¯¥æ¤åæ¹ç¨ï¼
107ï¼å¨æ¤åx~2+y~2/a~2=1(0<a<1)ä¸,è·é¡¶ç¹A(0,a)è·ç¦»æ大çç¹æ°å¥½æ¯å¦ä¸é¡¶ç¹A'(0,-a),æ±å®æ°açåå¼èå´ã
108ï¼å·²ç¥ç´çº¿y=kx+2åæ¤å2x^2+3y^2=6æä¸¤ä¸ªå ¬å ±ç¹ï¼åkçåå¼èå´æ¯ï¼ ï¼ã
109ï¼æ¤åçä¸å¿å¨åç¹,ç¦ç¹å¨Xè½´ä¸,并è¿ç¹M1(6,4)åM2(8,-3),æ±æ¤åçæ åæ¹ç¨.
110ï¼ä¸å¨ç¹å°å®ç¹A(3,0)çè·ç¦»åå®å°ç´çº¿X=12çè·ç¦»çæ¯ä¸º1/2,æ±å¨ç¹ç轨迹æ¹ç¨.
111ï¼å¨å¹³é¢ç´è§åæ ç³»ä¸ï¼è¥æ¹ç¨m(x^2+y^2+2y+1)=(x-2y+3)^2表示çæ²çº¿ä¸ºæ¤åï¼åå®æ°mçåå¼èå´æ¯ï¼ ï¼ã
112ï¼ä¸ä¸ªæ¤åçé¿è½´é¿æ¯çè½´é¿ç两å ï¼æ±è¿æ¤å离å¿çã
113ï¼åæ²çº¿çä¸å¿å¨åæ åç¹ï¼ 离å¿ççäº2 ï¼ä¸ä¸ªç¦ç¹åæ 为(2,0)ï¼ æ±åæ²çº¿æ¹ç¨ã
114ï¼å·²ç¥æ¤åa^2*x^2-0.5a*y^2=1çä¸ä¸ªç¦ç¹åæ æ¯(-2,0)ï¼æ±açå¼ã
115ãç»è¿æ¤åx^2/4+y^2/3=1çä¸ä¸ªç¦ç¹F1çç´çº¿äº¤æ¤åäºAåB两ç¹,F2æ¯å¦ä¸ä¸ªç¦ç¹,åä¸è§å½¢ABF2çå¨é¿æ¯ï¼ ï¼ã
116ï¼æ¤åx~2/a~2+y~2=1(a>1)çä¸ä¸ªç¦ç¹ä¸ºF,ç¹På¨æ¤åä¸,ä¸/OP/=/OF/(O为åæ åç¹),åâ³OPFçé¢ç§¯Sæ¯ï¼ ï¼ã
117ï¼ä¸æ¤åx^2/4+y^2=1å ±ç¦ç¹ä¸è¿ç¹Q(2,1)çåæ²çº¿æ¹ç¨æ¯______ã
118ï¼ç´çº¿y=kx-1åæ¤åx~2/4 + y~2/(âa)~2=1 ç¸å ï¼æ±kåaçåå¼èå´ã
119ï¼æ¤åx~2/25 + y~2/9=1ä¸æ3个ç¹Aï¼x1ï¼y1)ï¼ B(4ï¼9/5 )ï¼ C(x2ï¼y2) å®ä»¬åå³ç¦ç¹ï¼4,0)è·ç¦»æçå·®æ°å ï¼æ±X1+X2çå¼ã
120ï¼è¥ç¹A(0,7)ï¼B(0,-7)ï¼C(æ ¹2ï¼2ï¼ï¼ä»¥C为ä¸ç¦ç¹ä½è¿Aï¼Bçæ¤åï¼æ±å¦ä¸ç¦ç¹ç轨迹æ¹ç¨ã
121ï¼ä»¥ï¼ï¼1ï¼2ï¼ï¼ï¼7ï¼2ï¼ä¸ºç¦ç¹ï¼çè½´é¿ä¸º6çæ¤åæ¹ç¨æ¯ï¼ ï¼ã
122ï¼å·²ç¥F1ãF2æ¯æ¤åx~2/a~2+y~2/(10-a)~2=1(5<a<10)ç两个ç¦ç¹ï¼Bæ¯çè½´çä¸ä¸ªç«¯ç¹ï¼åâ³F1BF2çé¢ç§¯çæ大å¼æ¯å¤å°ï¼
123ï¼è®¾æç为K1çç´çº¿L交æ¤åX~2ï¼2ï¼Y~2ï¼1äºAï¼B两ç¹ï¼ç¹M为弦ABçä¸ç¹ï¼ç´çº¿OMçæç为K2ï¼O为åæ åç¹ï¼å设K1ï¼K2é½åå¨ï¼ æ±K1*K2çå¼ã
124ï¼è®¾æ¤åx~2/a~2+y~2/b~2=1ï¼éè¿æ¤åå¤ä¸ç¹(m,n)æ±å°æ¤åçå¾æè¿åæè¿ç¹?
125ï¼ä¾å¦,åæ²çº¿ x^2/4-y^2/12=1 ï¼å®ç两个顶ç¹çåæ æ¯(-2.0)ä¸(2.0)ï¼é£ä¹å¤æå¨åæ²çº¿çå·¦æ¯ä¸å³åªåºè¯¥è®©Xåå«æ»¡è¶³ä»ä¹æ¡ä»¶å?
126ï¼å·²ç¥åæ²çº¿y=k/xè¿ç¹Aï¼2ï¼3ï¼ï¼ï¼1ï¼è¥Aå ³äºç´çº¿y=xç对称ç¹ä¸ºBï¼è¯å¤æç¹Bæ¯å¦å¨åæ²çº¿y=k/xä¸ï¼å¹¶è¯´æçç±ï¼ï¼2ï¼æ±ä¸è§å½¢OABçé¢ç§¯
127ï¼ä¸å¿å¨åç¹,ä¸ä¸ªç¦ç¹ä¸ºF(1,0)çåæ²çº¿,å ¶å®é¿è½´é¿ä¸èè½´é¿ä¹æ¯ä¸ºm,æ±æ¤åæ²çº¿çæ åæ¹ç¨ã
128ï¼å·²ç¥åæ²çº¿ç离å¿ç为2,åå®ç两æ¡æ¸è¿çº¿ç夹è§ä¸º_____ã
129ï¼åæ²çº¿x~2/16-y~2/9=1ï¼å ¶ä¸æä¸ç¹Pï¼è§F1PF2çäº60度ï¼æ±ä¸è§å½¢F1PF2çé¢ç§¯ã
130ï¼åæ²çº¿X~2/a~2âY~2/b~2=1(a>1,b>0)çç¦è·2C,ç´çº¿Lè¿(a,0)(b,0)ä¸(1,0)å°ç´çº¿Lçè·ç¦»ä¸ç¹(-1,0)å°Lè·ç¦»ä¹åS>=4C/5,æ±åæ²çº¿ç离å¿çeçåå¼èå´?
131ï¼è®¾ç¹På°ç¹Mï¼-1ï¼0ï¼ãNï¼1ï¼0ï¼è·ç¦»ä¹å·®ä¸º2m,å°Xè½´ãYè½´è·ç¦»ä¹æ¯ä¸º2ãæ±mçåå¼èå´ã
132ï¼ä¸ä¸ªæ£ä¸è§å½¢çä¸ä¸ªé¡¶ç¹åå¨åæ²çº¿x^2-ay^2=1çå³æ¯ä¸,å ¶ä¸ä¸ä¸ªé¡¶ç¹ä¸åæ²çº¿çå³é¡¶ç¹éå,åå®æ°açåå¼èå´?
133ï¼è®¾F1 ï¼F2æ¯åæ²çº¿X~2/4-Y~2=1 ç两个ç¦ç¹ï¼ç¹På¨åæ²çº¿ä¸ï¼ä¸PF1åç´PF2ï¼åPF1*PF2çäºï¼ ï¼ã [çæ¡ï¼2]
134ï¼ç´çº¿Yï¼aXï¼1ï¼0ä¸åæ²çº¿3Xï¼¾2ï¼Yï¼¾2=1ç¸äº¤äºAï¼B两ç¹ï¼ï¼1ï¼å½a为ä½å¼æ¶ï¼Aï¼Bå¨åæ²çº¿çåä¸æ¯ä¸ï¼å½a为ä½å¼æ¶ï¼Aï¼Båå«å¨åæ²çº¿ç两æ¯ä¸ï¼ï¼2ï¼å½a为ä½å¼æ¶ï¼ä»¥AB为ç´å¾ä¸ååè¿åæ åç¹ï¼
135ï¼åæ²çº¿x²-y²=a²(a>0)çå·¦ï¼å³é¡¶ç¹åå«ä¸ºAï¼Bï¼ç´çº¿låç´äºå®è½´æå¨çç´çº¿ä¸ä¸åæ²çº¿äº¤äºPï¼Q两ç¹ï¼æ±è¯ï¼â PAQ+â PBQ=180°ã
136ï¼å·²ç¥åæ²çº¿mï¼x^2/a^2-y^2/b^2=1(a>0,b>0)ï¼ç¦»å¿çe=2ï¼çº¿æ®µABçåç´å¹³å线为x-y-2=0ï¼ä¸|AB|=æ ¹46
ï¼1ï¼ æ±åæ²çº¿ç»è¿äºï¼å象éçæ¸è¿çº¿çå¾æè§
ï¼2ï¼ æ±çº¿æ®µABä¸ç¹Cçåæ
ï¼3ï¼ æ±ç´çº¿ABçæ¹ç¨
ï¼4ï¼ æ±åæ²çº¿mçæ¹ç¨
137ï¼å ³äºxy=1çé®é¢ï¼ä¸å¤ªæç½ ï¼æ¤ååæ²çº¿ç离å¿çåæ¯ä¼ï¼è¿ä¸ªç¦»å¿çæ¯ä»£è¡¨çæ¯ä»ä¹æä¹å¢ï¼
138ï¼è¯·é®ä¸ä¸ï¼å¨åæ²çº¿ä¸è¿ä¸ç¦ä¸åæ²çº¿ç¸äº¤çç´çº¿ï¼Kä¸çäº0ï¼ï¼éå¾é¿æ¯æççåï¼
139ï¼è®¾ç´çº¿Lçæ¹ç¨ä¸ºy=kx-1,çè½´åæ²çº¿Cçä¸å¿å¨åç¹ï¼å³ç¦ç¹åæ 为ï¼æ ¹2ï¼0ï¼ï¼ç´çº¿Lä¸åæ²çº¿å³æ¯äº¤äºä¸åç¹Aï¼Bï¼è®¾å¼¦ABçä¸ç¹åæ 为Mï¼Qç¹åæ 为ï¼-1ï¼0ï¼ï¼æ±ç´çº¿QMå¨yè½´ä¸çæªè·çåå¼èå´ã
140ï¼è®¾Pæ¯åæ²çº¿X~2/3-Y~2=1çå³æ¯ä¸ä¸ä¸ªå¨ç¹ï¼Fæ¯åæ²çº¿çå³ç¦ç¹ï¼å·²ç¥Aç¹çåæ æ¯(3,1)ï¼å|PA|+|PF|çæå°å¼æ¯_______ã
141ï¼Fæ¯åæ²çº¿X~2/16-Y~2/9=1å³ç¦ç¹ï¼Mæ¯åæ²çº¿å³æ¯ä¸ä¸å¨ç¹ï¼å®ç¹Açåæ 为(5,4)ï¼å4|MF|-5|MA|çæ大å¼æ¯______ã
142ï¼å·²ç¥çè½´åæ²çº¿ç»è¿ç¹ï¼-3ï¼2ï¼ä¸å¯¹ç§°è½´é½å¨åæ è½´ä¸ï¼æ±å®çæ¹ç¨ã
143ï¼å·²ç¥åæ²çº¿(x-h)(y-k)=a(aä¸ä¸º0)çæ°´å¹³æ¸è¿çº¿y=k,ç«ç´æ¸è¿çº¿ä¸ºx=h,ä¸å¿ä¸ºï¼h,k),è¥åæ²çº¿y=x/(x-1) çç¹å°å®çæ°´å¹³æ¸è¿çº¿ï¼ç«ç´æ¸è¿çº¿ï¼ä¸å¿çè·ç¦»åå«æ¯d1,d2,d3.åd1+d2+d3çæå°è·ç¦»ä¸ºï¼ ï¼ã
A4ãããB2ï¼æ ¹2ããC3ï¼æ ¹2ããD3
144ï¼éè¿ä¸ç¹(1,3)ä½ä¸æ¡ç´çº¿,ååæ²çº¿y*y=-16xäºAB两ç¹.æ±åç¹åæ .
145ï¼ç´çº¿y-ax-1=0 ååæ²çº¿3x^2-y^2=1ç¸äº¤äºA ï¼Bä¸¤ç¹ a为ä½å¼æ¶ã以AB为ç´å¾çåç»è¿åç¹ï¼
146ãåæ²çº¿ x^2-y^2=1 ï¼ç´çº¿l ï¼y=kx+m (kä¸ä¸º0)ä¸åæ²çº¿äº¤äºA,B.æD(0,-1),ä¸æ|AD|=|BD|,æ±mèå´ã
147ï¼å·²ç¥ç´çº¿ï¼l1:5x+3y=0ål2:5x-3y=0ï¼å¦æ以ç´çº¿l1ål2为æ¸è¿çº¿çåæ²çº¿ç»è¿ç¹Mï¼1ï¼3ï¼ï¼æ±æ¤åæ²çº¿çæ åæ¹ç¨ã
148ï¼ç»è¿ç´çº¿L:x+y-2=0ä¸ä¸ç¹mä¸ä»¥åæ²çº¿X~2/12-Y~2/4=1çç¦ç¹ä¸ºç¦ç¹ä½åæ²çº¿ï¼å½må¨ä½å¤æ¶ï¼æä½åæ²çº¿å®è½´é¿æé¿ï¼å¹¶æ±åºå ·ææé¿å®è½´çåæ²çº¿æ¹ç¨ã
149ï¼ä¸¤å®ç¹ABè·ç¦»ä¸º6,å¨ç¹M满足è§MBA=2è§MAB,æ±å¨ç¹Mç轨迹æ¹ç¨.
150ï¼å·²ç¥åæ²çº¿çå®è½´2aï¼8ï¼ç´çº¿MNè¿ç¦ç¹F1交åæ²çº¿äºMï¼Nï¼ MNï¼7ï¼æ±ä¸è§å½¢MNF2ï¼F2为å¦ä¸ç¦ç¹)çå¨é¿ã
151ï¼è¿ç¹P(4,4)ä¸åæ²çº¿x^2/16-y^2/19=1åªæä¸ä¸ªå ¬å ±ç¹çç´çº¿æå æ¡?
152ï¼å·²ç¥åæ²çº¿ä¸¤æ¡æ¸è¿çº¿æ¹ç¨ä¸ºY=±2X,ç´çº¿Y=X+3被åæ²çº¿æªå¾å¼¦é¿ä¸º8,ååæ²çº¿æ¹ç¨ä¸º?
153ï¼ç´çº¿y=kx+m(kä¸çäº0,mä¸çäº0)ä¸åæ²çº¿x~2/3 ây~2 =1交äºä¸å两ç¹CãD åCãD两ç¹é½å¨ä»¥A(0,-1)为åå¿çåä¸ä¸ªåä¸,æ±mçåå¼èå´.
154ï¼å·²ç¥åæ²çº¿çä¸å¿å¨åæ åç¹,å³ç¦ç¹F(2,0),以F为åå¿,OF为åå¾ä½åä¸åæ²çº¿çä¸æ¡æ¸è¿çº¿äº¤ä¸Oï¼A两ç¹ï¼è¥2â¤OAâ¤2â2
ï¼1ï¼æ±åæ²çº¿ç离å¿çeçåå¼èå´
ï¼2ï¼è¿Fçç´çº¿ä¸åæ²çº¿çå³æ¯äº¤ä¸MãN两ç¹ä¸MF=2FNï¼æ³¨ï¼MFä¸FN为åéï¼ï¼æ±ç´çº¿MNçæçæå°æ¶åæ²çº¿çæ¹ç¨ã
155ï¼å·²ç¥åæ²çº¿Cç两æ¡æ¸è¿çº¿è¿åç¹,ä¸ä¸å ¶å³é¡¶ç¹A2(æ ¹å·2,0)为åå¿,1为åå¾çåé½ç¸å.è¥è®¾æ²çº¿Cç左顶ç¹ä¸ºA1,Pä¸ºå ¶å³æ¯ä¸ä»»ä¸ç¹(ä¸A2ä¸éå)è¯å¤æç´çº¿A1Pä¸A2Pçç¡®å¾æè§ä¹é´çå ³ç³»ã
156ï¼è®¾ç¹Pæ¯åæ²çº¿X~2/16-Y~2/9=1å³æ¯ä¸ä¸ç¹ï¼Fæ¯è¯¥åæ²çº¿çå³ç¦ç¹ï¼Mæ¯PFçä¸ç¹,O为åæ åç¹ï¼ä¸|OM|=6,åç¹På°è¯¥åæ²çº¿å³å线çè·ç¦»ä¸º( )ã
A.5 B.16/5 C.15 D.48/5
157ï¼è¿ç¹N(0,-2)ä½ç´çº¿l交åæ²çº¿Cï¼x~2ï¼y~2ï¼1äºAï¼B以OAï¼OB为é»è¾¹åå¹³è¡å边形OAPBï¼æ±ç¹Pç轨迹æ¹ç¨ï¼
158ï¼å·²ç¥MåN两ç¹å ³äºY轴对称,ä¸ç¹Må¨åæ²çº¿Y=1/2X,ç¹Nå¨Y=X+3ä¸,设ç¹Mçåæ 为(A,B),æ±æ ¹å·[A~2+B~2]çå¼ã
159ï¼åæ²çº¿çä¸å¿å¨åæ åç¹,离å¿ççäº2,ä¸ä¸ªç¦ç¹çåæ 为(2,0),åæ¤åæ²çº¿çæ¹ç¨æ¯ä»ä¹?
160ï¼åæ²çº¿y=2/xçç¦ç¹æ¯å¤å°ï¼
161ï¼å¨åæ²çº¿x^2-y^2=1çå³æ¯ä¸çä¸ç¹P(a,b)å°ç´çº¿y=xçè·ç¦»ä¸ºæ ¹2,æ±aåbçå¼ã
162ãå·²ç¥ä¸è§å½¢ç两个顶ç¹b(-5,0),C(5,0)è¾¹AB,ACæå¨ç´çº¿æçä¹ç§¯ä¸º1/7,æ±ç¬¬ä¸ä¸ªé¡¶ç¹Aç轨迹æ¹ç¨ã
163ï¼æ±ç»è¿å®ç¹Mï¼-3ï¼2ï¼ï¼ä¸ä»¥ç´çº¿X=0为左å线ï¼ç¦»å¿çe=2çåæ²çº¿å³ç¦ç¹ç轨迹æ¹ç¨ã
164ï¼å设ä¸ä¸ªæ¤åCï¼x^2/a^2+y^2/b^2=1(a>b>0)çå·¦å³ç¦ç¹åå«æ¯F1åF2.è¿å³ç¦ç¹F2ä¸xè½´åç´çç´çº¿lä¸æ¤åCç¸äº¤,å ¶ä¸ä¸ä¸ªç¦ç¹ä¸ºM(æ ¹2,1)
ï¼1ï¼ æ±æ¤åCçæ¹ç¨
ï¼2ï¼ è¥p为æ¤åCä¸ä¸ç¹,PF1åç´PF2,æ±ä¸è§å½¢F1PF2çé¢ç§¯.
165ï¼å¨ç´è§åæ ç³»ä¸ï¼ç´çº¿y=x+mä¸åæ²çº¿y=m/xå¨ç¬¬ä¸è±¡é交äºç¹Aï¼ä¸x轴交äºç¹Cï¼ABåç´xè½´ï¼å足为Bï¼ä¸ä¸è§å½¢AOBçé¢ç§¯çäº1ã
ï¼1ï¼æ±må¾å¼ï¼2ï¼æ±ä¸è§å½¢ABCçé¢ç§¯
166ï¼ä»¥ç¥F1ï¼F2åå«æ¯åæ²çº¿x^2/a^2-y^2/b^2=1(a>0,b>0)çå·¦å³ç¦ç¹ï¼P为åæ²çº¿å·¦æ¯ä¸ä»»æä¸ç¹ï¼è¥|PF2|^2/|PF1|çæå°å¼ä¸º8a,å该åæ²çº¿ç¦»å¿çeçåå¼èå´æ¯? çæ¡æ¯ï¼ï¼1ï¼3ã
167ï¼çè½´åæ²çº¿ï¼ ç¦ç¹F1ï¼-2ï¼2ï¼ï¼F2ï¼4ï¼-4ï¼ï¼æ±åæ²çº¿ï¼
168ï¼å·²ç¥åæ²çº¿X^2/a^2-Y^2/b^2=1(a>0,b>0)ç左顶ç¹ä¸ºA(-1,0),è¿ç¹Aä½ä¸¤æ¡ç´çº¿åå«äº¤åæ²çº¿çå³æ¯äºB(X1,Y1)ãCï¼X2ï¼Y2ï¼ä¸¤ç¹ï¼ä¸ä¸è§å½¢ABC为æ£ä¸è§å½¢ã
ï¼1ï¼è¯æï¼BãC两ç¹å ³äºX轴对称
ï¼2ï¼è®¾X1>2ï¼æ±bçåå¼èå´
169ãx^2+xy-6y^2-20y-20x+k=0 表示两æ¡ç´çº¿,æ±è¿ä¸¤æ¡ç´çº¿ã
2ï¼å·²ç¥F1ï¼F2æ¯æ¤å x~2/100+y~2/64=1 ç两个ç¦ç¹ï¼Pæ¯æ¤åä¸çä»»ä¸ç¹ï¼ä¸è§F1PF2=60度ï¼æ±ä¸è§å½¢F1PF2çé¢ç§¯ã
3ï¼å·²ç¥æ¤å x^2/a^2+y^2/b^2=1 åæ¤åä¸ä¸ä¸ªå®ç¹ P(m,n) æ¤åä¸åæå¦ä¸¤ç¹ A,B 满足 PAåç´äºPBãæ±è¯:ç´çº¿ABè¿ä¸å®ç¹ã
4ï¼æ±ä¸å¿å¨åæ åç¹,åæ 轴为对称轴è¿ç¹a(4,1)ä¸ä¸ç´çº¿x+4yâ10=0æä¸åªæä¸ä¸ªå ¬å ±ç¹çæ¤åæ¹ç¨ã
5ï¼è®¾A1ï¼A2åå«ä¸ºæ¤åx^2/a^2+y^2/b^2ï¼1å¨xè½´ä¸ç两个端ç¹ãP为æ¤åä¸ä¸å¨ç¹ï¼F为æ¤åçå³ç¦ç¹ãç»åºæ¤åçå³å线ï¼åå«è¿æ¥A1-Pï¼A2-Pï¼å»¶é¿åä¸å线çç¦ç¹åå«ä¸ºMNãæ±è§MFNç度æ°ã
6ï¼æ¤åEçä¸å¿å¨åç¹O,ç¦ç¹å¨xè½´ä¸,é«å¿çe=æ ¹å·ä¸(2/3),è¿ç¹C(-1,0)çç´çº¿L交æ¤åäºA,B两ç¹,ä¸CAåé=λBCåé (λâ¥2).
(1).è¥Î»ä¸ºå¸¸æ°,ç´çº¿Lçæç为K(Kä¸ä¸º0),ååºâ³OABçé¢ç§¯Så ³äºKç表达è¯f(K)
(2).è¥Î»ä¸ºå¸¸æ°,å½Sæ大æ¶,æ±æ¤åEçæ¹ç¨
7ï¼å¨æ¤åx~2/25+y~2/9=1ä¸ä¸ç¹p,使å®å°å·¦ç¦ç¹çè·ç¦»æ¯å®å°å³ç¦ç¹è·ç¦»ç2å.
8ï¼å¨æ¤å x~2/45 + y~2/20 ä¸æ±ä¸ç¹ï¼ä½¿å®ä¸ä¸¤ç¦ç¹çè¿çº¿äºç¸åç´ã
9ï¼è¿æ¤åX~2/a~2+Y~2/b~2=1[0<b<a]ä¸å¿çç´çº¿ä¸æ¤å交äºA,B两ç¹,å³ç¦ç¹ä¸ºF(c,0),åä¸è§å½¢ABF2çæ大é¢ç§¯æ¯ï¼ ï¼ã
A ab B ac C bc D b~2
10ï¼ç´çº¿y=x-1åæ¤åx^2/m+y^2/(m-1)=1(m大äº1ï¼äº¤äºAãBï¼ä»¥AB为ç´å¾çåè¿æ¤åçç¦ç¹Fï¼æ±å®æ°mçå¼ã
11ï¼ä¸ä¸ªé¿è½´ä¸º2a,ç轴为2bçæ¤åï¼å¨ç¬¬ä¸è±¡éå æ»å¨ï¼å¹¶å§ç»ä¸Xè½´ï¼Yè½´é½ç¸åãæ±è¯¥æ¤åä¸å¿Cç轨迹æ¹ç¨ã
12ï¼å·²ç¥ä¸¤å®åC1:ï¼X-2ï¼~2+Y~2=1ï¼C2ï¼ï¼X+2ï¼~2+Y~2=81ï¼ä¸å¨åCä¸C1å¤åï¼ä¸åC2å åï¼æ±å¨ååå¿ç轨迹æ¹ç¨ã
13ï¼ä¸è§å½¢ABCç两个顶ç¹A.Bçåæ åå«æ¯(-5,0),(5,0),è¾¹AC,BCæå¨ç´çº¿çæçä¹ç§¯ä¸º-1/2,æ±é¡¶ç¹Cç轨迹æ¹ç¨.
14ï¼å·²ç¥æ¤åçç¦ç¹å¨æ¨ªè½´ä¸ï¼è¿ç¦ç¹Fçç´çº¿äº¤æ¤åäºPQ两ç¹ï¼ä¸æ»¡è¶³OPâ¥OQï¼æ±æ¤å离å¿ççåå¼èå´
15ï¼æ¤åX~2/a~2+Y~2/b~2=1(a>b>0)ååX~2+Y~2=(b/2 + C)~2,交äºå个ä¸åç¹,åæ¤åç离å¿ççåå¼èå´?
16ï¼è®¾æ¤åä¸åæ²çº¿æå ±åçç¦ç¹F1ï¼ï¼4ï¼0ï¼åF2ï¼4ï¼0ï¼ï¼å¹¶ä¸æ¤åçé¿è½´é¿æ¯åæ²çº¿å®è½´é¿ç2åï¼è¯æ±æ¤åä¸åæ²çº¿äº¤ç¹ç轨迹æ¹ç¨ã
17ï¼è¥æ¤åX~2/4+Y~2/3=1ä¸æä¸åçç¹PãQå ³äºç´çº¿y=4x+m对称ï¼æ±mçåå¼èå´ï¼
18ï¼æ¤å X^2/A^2+Y^2/B^2=1 (A>B>1)ä¸ä¸¤ç¹M,N.MN=L (å®é¿)ï¼L>2*B^2/A. æ±MNä¸ç¹æ¨ªåæ çæ大å¼.ç¨A,B,L表示.
19ï¼æ¤åx~2/9+y~2/4=1, ç¦ç¹ä¸ºF1,F2,P为æ¤åä¸ä¸å¨ç¹,åä¸è§PF1F2é¢ç§¯çæ大å¼æ¯å¤å°?
20ï¼æ¤åçé¢ç§¯å ¬å¼æ¯ä»ä¹ï¼
21ï¼è¿æ¤åx~2/a~2+y~2/b~2=1(a>b>0)çå³ç¦ç¹Fçä»»æç´çº¿äº¤yè½´äºPç¹ ï¼äº¤æ¤åäºM,N æ±è¯: PM/MF+PN/NF为å®å¼ã
22ï¼ä¸æç为3/4çç´çº¿è¿ä¸ä¸å¿å¨åç¹çæ¤åå·¦ç¦ç¹ï¼ä¸ä¸æ¤åçäºäº¤ç¹ä¸ï¼æä¸äº¤ç¹çºµåæ 为3ï¼å·²ç¥æ¤åå³ç¦ç¹å°ç´çº¿çè·ç¦»ä¸º12/5ï¼æ±æ¤åçæ åæ¹ç¨ï¼
23ï¼è¿åx~2+y~2=4å ä¸ç¹a(1,0)ååç弦,æ±è¿äºå¼¦çä¸ç¹mç轨迹æ¹ç¨.
24ï¼æ¤å:X^2/a^2+y^2/b^2=1(a>b>0)çå·¦ï¼å³ç¦ç¹åå«æ¯F1,F2 å³ç¦ç¹ç顶ç¹ä¸ºA.M为æ¤åãC1ä¸ä»»æä¸ç¹ï¼ä¸MF1*MF2çæå°å¼æ¯3/4a^2
ï¼1ï¼æ±åæ²çº¿C2
ï¼2ï¼ä»¥æ¤åçC1çç¦ç¹ä¸ºé¡¶ç¹ï¼é¡¶ç¹ä¸ºç¦ç¹ï¼å¨ç¬¬ä¸è±¡éå ä»»ååæ²çº¿C2ä¸ä¸ç¹P,è¯é®æ¯å¦åå¨å¸¸æ°Q(Q>0).使å¾è§PAF1=Qåçè§PF1Aææç«ï¼
25ï¼è¿æ¤åå·¦ç¦ç¹Fä¸å¾æè§ä¸º3/Ïçç´çº¿äº¤æ¤åäºA,B两ç¹ï¼è¥|FA|=2|FB|ï¼åæ¤åç离å¿çæ¯ï¼ ï¼ã
26ï¼é®é¢ï¼ç¥éæ¤åçé¿è½´åçè½´ï¼æä¹æ±ç¦è·ï¼
27ï¼å·²ç¥æ¤åC x²/a²+y²/b²=1 设Aï¼X1ï¼Y1ï¼ï¼Bï¼X2ï¼Y2ï¼ï¼X1ä¸çäºX2ä¸Y1ä¸çäºY2ï¼ä¸ºæ¤åä¸ä¸¤ç¹ï¼Aï¼B两ç¹ç对称轴lå¨Xè½´ãYè½´ä¸çæªè·åå«ä¸ºmãn.æ±è¯ï¼ï¼a²-m²)/b²+(b²-n²)/a²>2
28ï¼æ¤åçæ¹ç¨æ¯x~2/4b~2+y~2/b~2=1 ï¼æ¤åä¸æä¸ç¹På°å³ç¦ç¹çè·ç¦»ä¸ºbï¼æ±På°å·¦å线çè·ç¦»ã
29ï¼å·²ç¥åCä¸åC1ï¼x~2+ (y-4)~2= 64å åï¼ä¸åC2ï¼x~2+ (y+4)~2= 4å¤åãæ±Cçåå¿è½¨è¿¹ã
30ï¼x^2/25+y^2/9=1 ï¼ç¹A(x1,y1),B(4,y2),C(x3,y3)å¨æ¤åä¸ï¼ F为å³ç¦ç¹ ï¼AF+CF=2BF ï¼æ±ACä¸ç¹è½¨è¿¹ã
31ï¼æ¤å两ç¦ç¹åä¸å¿å°ä¸¤å线çè·ç¦»åçåï¼åä¸ç¦ç¹ä¸ç轴两端ç¹è¿çº¿é´ç夹è§ä¸ºï¼ ï¼ã
32ï¼P为æ¤åä¸ä¸ç¹ï¼F₁ãF₂ 为æ¤åç¦ç¹ï¼Xè½´ä¸ï¼ï¼AãB为æ¤åå·¦ãå³é¡¶ç¹ï¼å½Pç¹ä¸ºæ¤åä¸é¡¶ç¹æä¸é¡¶ç¹æ¶ï¼è§F₁PF₂ãè§APB ææ大å¼ï¼
[S(F1PF2)=b^2*tan(è§F1PF2/2)]
33ï¼Pï¼xï¼yï¼ä¸ºæ¤åX~2ï¼3ï¼y~2ï¼1ä¸çç¹ï¼åPç¹å°ç´çº¿Xï¼Yï¼2çæ大è·ç¦»æ¯å¤å°ï¼
34ï¼è®¾æ¤åx~2/a~2+y~2/b~2=1(a>b>0)çå·¦å³ç¦ç¹åå«ä¸ºF1,F2,æ¤åä¸åå¨ç¹p,使è§F1pF2为éè§,æ±ç¦»å¿ççèå´ã
35ï¼ä¸é¢äººé å°çå«æçè¿è¡è½¨éå°ä»¥å°ççä¸å¿ä¸ºä¸ä¸ªç¦ç¹çæ¤åï¼è¿å°ç¹Aè·å°é¢439KMï¼è¿å°ç¹Bè·å°é¢2384KMï¼å°çåå¾çº¦ä¸º6371KM ï¼æ±å«æç轨éæ¹ç¨ã
36ï¼è®¾Aï¼X1ï¼Y1ï¼ä¸ºæ¤åX^2+2y^2=2ä¸çä»»ä¸ç¹ï¼è¿Aä½ä¸æ¡æç为-X1/2Y1çç´çº¿Lï¼å设d为åç¹å°Lçè·ç¦»ï¼r1ï¼r2åå«ä¸ºç¹å°ä¸¤ç¦è·çè·ç¦»ï¼æ±è¯æ ¹å·r1*æ ¹å·r2*d为å®å¼ã
37ï¼å¨ä¸è§å½¢ABCä¸ï¼Bï¼4ï¼0ï¼ï¼Cï¼-4ï¼0ï¼ï¼ç¹Aè¿å¨æ¶æ»¡è¶³sinA-sinB=1/2*sinAï¼æ±Aç¹ç轨迹ã [è¿æ¯ä¸ä¸ªå»é¤ä¸¤é¿è½´ç«¯ç¹çæ¤å]
38ï¼å·²ç¥ç¹Påæ æ¯ï¼-1ï¼-3ï¼ï¼F为æ¤åX^2/16+Y^2/12=1çå³ç¦ç¹ï¼ç¹Qå¨æ¤åä¸ç§»å¨ï¼å½|QF|+0.5|PQ|åæå°å¼æ¶ï¼æ±ç¹Qåæ ï¼å¹¶æ±å ¶æå°å¼ã
39ï¼å·²ç¥æ¤åX2/a2+Y2/b2=1(a>b>0)åç¹B(0,b)ï¼ Pæ¯æ¤åä¸å¨ç¹ï¼ æ±BPé¿åº¦çæ大å¼ã[è¦å类讨论
40ï¼è¿æ¤åå³ç¦ç¹Fä½å¾æè§ä¸º120°çç´çº¿äº¤æ¤åäºAãB两ç¹ï¼è¥|FA|=2|FB|åæ¤åç离å¿çæ¯ï¼ ï¼ã
41ï¼æ¤åæ¹ç¨x2ï¼4+y2ï¼3ï¼1ï¼å³ç¦ç¹F(1,0),ç¹P(1,1),Mç¹å¨æ¤åä¸ï¼æ±MP+2MFçæå°å¼ã
42ï¼A,B两个æ¹åå¸åº,ååæ¹åä»·ç¸å,ä½å¨æå°åºçå± æ°ä»ä¸¤å°è¿åååæ¶,æ¯åä½è·ç¦»çè¿è´¹ä¸å,Aå°è¿è´¹æ¯Bå°ç两å,å·²ç¥A,B两å°ç¸è·10å ¬é,é®:å± æ°å¦ä½éæ©è¿è´§å°ç¹,æè½ä½¿è¿è´¹æ便å®.
43ï¼è®¾F1,F2æ¯æ¤å(X^2)/4+(y^2)/3=1çå·¦å³ç¦ç¹,Aæ¯æ¤åä¸å¨ç¹,è¿F1ä½è§F1AF2çå¤è§çå¹³å线çå线,设å足为P,æ±Pç轨迹
44ï¼æ±ä»¥åç¹ä¸ºå³ç¦ç¹,ç´çº¿x=1为å³å线çå¨æ¤åç轴端ç¹ç轨迹æ¹ç¨ã
45ï¼è®¾M,N为æ¤åx^2/9+y^2/4=1ç两ç¦ç¹,Pæ¯æ¤åä¸çä¸ç¹,å·²ç¥P,M,Næ¯ä¸ä¸ªç´è§ä¸è§å½¢çä¸ä¸ªé¡¶ç¹ä¸|PM|>|PN|.æ±|PM|/|PN|çå¼.
46ã设å¨åPè¿å®ç¹A(-3,0),并ä¸å¨å®åB:(x-3)2+y2=64çå é¨ä¸å ¶å å,æ±å¨åçåå¿Pç轨迹æ¹ç¨?
47ï¼å·²ç¥æ¤åx^2/6+y^2/2=1,对åºäºç¦ç¹F(c,0)çå线lä¸xè½´ç¸äº¤äºç¹A,è¿Açç´çº¿ä¸æ¤å交äºP,Q两ç¹,è¥PQç´çº¿çæç为[æ ¹3]/3,æ±ä¸è§å½¢FPQçé¢ç§¯ã
48ï¼è¿æ¤åçå·¦ç¦ç¹ä½åç´äºXè½´ç´çº¿äº¤æ¤åä¸Mï¼ä¸æ¤åçä¸é¡¶ç¹ä¸å³é¡¶ç¹è¿çº¿å¹³è¡ä¸MOï¼æ±æ¤åç离å¿çã
49ï¼å·²ç¥æ¤åï¼X~2/4+Y~2=1ï¼æç´çº¿Lï¼X=Tï¼T为大äº2çå®å¼ï¼ä¸X轴交äºç¹Tï¼P为Lä¸å¼äºTçä»»æä¸ç¹ï¼A1,A2æ¯æ¤åå·¦å³ç«¯ç¹ï¼ç´çº¿PA1ï¼PA2åå«ä¸æ¤åC交äºM.Nï¼é®ç´çº¿MNæ¯å¦ç»è¿Xè½´ä¸çä¸ä¸ªå®ç¹ï¼å¹¶è¯æä½ çç»è®ºã
[æ¤å®ç¹å¨é¿è½´å»¶é¿çº¿ä¸.]
å¦æä½ äºè§£æç¹æ线åå°å½±æ¹æ³çè¯,å¯ä»¥èèå ä½çè¯æ³.
ä¸è¬å:ç´çº¿Låç´äºæ¤åçé¿è½´....(åé¢çååé¢ç¸å)..
é¦å è¯æ对åçæ å½¢æç«,è¿éè¦æç¹æ线çç论.
ç¶åææ´ä¸ªå¾æ²¿ç´å¾æ¹åæ伸,æ¤ååè¿ç¨ä¸,ç¹çº¿çç»åæ§ä¿æä¸åã
50ï¼è®¾æ¤åä¸åæ²çº¿æå ±åç¦ç¹f(-4,0)åF(4,0)ï¼å¹¶ä¸æ¤åçé¿è½´é¿æ¯åæ²çº¿å®è½´é¿çäºåï¼è¯æ±æ¤åä¸åæ²çº¿äº¤ç¹ç轨迹æ¹ç¨ã
51ï¼å·²ç¥æ¤åCçä¸å¿å¨åç¹ï¼ç¦ç¹å¨è½´ä¸ï¼ç¦»å¿çE=1/2ï¼ä¸ç»è¿ç¹Mï¼-1ï¼3/2ï¼ãï¼1ï¼æ±æ¤åCçæ¹ç¨ï¼ï¼2ï¼è¥æ¤åCä¸æä¸åç两ç¹Pï¼Qå ³äºç´çº¿Y=4X+M对称ï¼æ±Mçåå¼èå´ã
52ï¼æ¤åæ¹ç¨ä¸º x~2/25 + y~2/16 = 1ï¼ æ¤åå ä¸å®ç¹Aï¼2ï¼1ï¼ ï¼å¨æ¤åä¸æ±ä¸ç¹Bï¼æ¯çº¿æ®µABçè·ç¦»æ大ã[å°é¾]
53ï¼xy=1ç离å¿ç为ä»ä¹çäºæ ¹å·2
54ï¼å·²ç¥æ¤åçé¿åè½´æ¯çåè½´ç3åï¼è¿å·¦ç¦ç¹å¾æè§ä¸º30度ç弦é¿ä¸º2ï¼åæ¤æ¤åçæ åæ¹ç¨ä¸ºï¼ ï¼ã
55ï¼å¨æ¤åx^2/a^2+y^2/b^2=1ä¸ï¼å½ä¸æ¡ç´çº¿ç©¿è¿å®æ两交ç¹Aï¼ B ï¼ è¿åå¿ O åæ¤åå 弦ABçä¸ç¹C ï¼ é£ä¹ç´çº¿ABæçä¸OCæçä¹ç§¯çäº âb~2/a~2ã
56ï¼å¨æ¤åx^2/a^2+y^2/b^2=1å ä½ä¸ä¸ªå æ¥ç©å½¢ï¼è¯é®é¿å®½åæ¯å¤å°æ¶ï¼é¢ç§¯æ大ï¼é¢ç§¯å¼æ¯å¤å°ï¼
57ï¼è®¾Aï¼Bæ¯æ¤å3x^2+y^2=pä¸ä¸¤ç¹ï¼ç¹Nï¼1ï¼3ï¼æ¯çº¿æ®µABçä¸ç¹ï¼çº¿æ®µABçåç´å¹³å线ä¸æ¤å交äºCD两ç¹ï¼è¯ç¡®å®pçèå´ï¼ä½¿ABCDåç¹å ±åã
58ï¼æ¤åçç¦ç¹F1,F2,è¿ç¦ç¹ä½ç´çº¿ä¸æ¤åç¸äº¤ï¼è¢«æ¤åæªå¾çæç线段MN为3/5,ä¸è§å½¢MF2Nçå¨é¿ä¸º20ï¼åæ¤åç离å¿çæ¯ï¼ ï¼ã
59ï¼æ¤å X~2/4+y~2/2=1ä¸.è¿ç¹P(1ï¼1)ç弦被Pç¹å¹³å,æ±æ¤å¼¦æå¨çç´çº¿æ¹ç¨å弦é¿ã
60ï¼å·²ç¥ç¹Aï¼4ï¼0ï¼åBï¼2ï¼2ï¼ï¼ç¹Mæ¯æ¤åX^2/25+Y^2/9=1ä¸çå¨ç¹ï¼åMA+MBçæ大å¼æ¯ï¼ ï¼ã
61ï¼æå¨é¢ä¹ é«äºä¸ç解æå ä½ï¼å¨æ¤åé书ä¸åªè®²äºæ²¡ææ转è¿çæ¤åæ¹ç¨ï¼æçå°ä¸é¢ æ¯å¦ä¸¤ä¸ªç¦ç¹æ¯ï¼1ï¼1ï¼åï¼-1ï¼-1ï¼ ä»»ææ¤åä¸ä¸ç¹å°ä¸¤ç¦ç¹è·ç¦»å为4ï¼æ±è¿ä¸ªæ¤åçæ¹ç¨ï¼æä¹åï¼
62ï¼ç¹Må°ç¹A(-4,0)ä¸ç¹B(4,0)çè·ç¦»çå为12,æ±ç¹Mç轨迹æ¹ç¨ã
63ï¼ç»è¿ç¹Pï¼ï¼3ï¼2ï¼ä¸ä¸ï¼X~2ï¼9ï¼Y~2ï¼4ï¼1æç¸åçç¦ç¹çæ¤åæ¹ç¨ï¼
64ï¼æ¤åx^2/100+y^2/64=1çç¦ç¹ä¸ºaï¼bï¼æ¤åä¸çç¹p满足è§apbï¼60度ï¼åé¢ç§¯apbæ¯å¤å°ï¼
65ï¼æ±ç»è¿ç¹M(1,2),以y轴为å线ï¼ç¦»å¿ç为0.5çæ¤åçå·¦å®ç¹ç轨迹æ¹ç¨ã
66ãæ¤å X~2/4+Y`2=1 ä¸Xè½´ç交ç¹ä¸ºA(2,0) B(-2,0),ä¸Yè½´å¹³è¡çç´çº¿äº¤è¯¥æ¤åäºP,Q两ç¹ï¼æ±APåBQ交ç¹mçæ²çº¿æ¹ç¨ã
67ãå·²ç¥ç´çº¿Y=X+Måæ²çº¿ X~2+2Y~2+4Y-1=0,交äºA,BãPæ¯è¿æ¡ç´çº¿ä¸çä¸ç¹ï¼ä¸âPAâ*âPBâ=2 ï¼æ±å½Mååæ¶ç¹Pç轨迹æ¹ç¨ï¼å¹¶è¯´æå½¢ç¶ã
68ãæ±ç»è¿åç¹ï¼ä»¥F(2,0)为å®çä¸ä¸ªç¦ç¹ï¼é¿è½´2a=bçæ¤åä¸å¿ç轨迹æ¹ç¨ã
69ãå·²ç¥ä¸¤åC1:X~2+Y~2+6Y=0,åC2:X~2+Y~2-6X-40=0ãæ±ä¸ä¸åå åï¼ä¸ä¸åå¤åçå¨ååå¿ç轨迹æ¹ç¨ã
70ãå·²ç¥ä¸¤åC1:(X-4)~2+Y~2=169 ï¼C2:ï¼X+4ï¼~2+Y~2=9ï¼å¨åå¨C1å é¨ä¸ååC1ç¸å åï¼ä¸C2ç¸å¤åï¼æ±å¨ååå¿ç轨迹æ¹ç¨ã
71ãæ¤åX~2/a~2+y~2/b~2=1 å æ¥ä¸è§å½¢ABCï¼å®çä¸è¾¹BCä¸é¿è½´éåï¼Aå¨æ¤åä¸è¿å¨ï¼è¯æ±ä¸è§å½¢ABCä¸å¿ç轨迹ã
72ï¼æ¤å两ç¦ç¹åä¸å¿å°ä¸¤å线é´çè·ç¦»åçåï¼åä¸ç¦ç¹ä¸ç轴两端ç¹è¿æ¥ç夹è§æ¯å¤å°ï¼
73ãæ¤åX~2/4 + Y~2/3 =1,ç¡®å®Mçå±æèå´ä¼¼ç对äºç´çº¿Y=4MX+Mæ¤åä¸æä¸åç两ç¹å ³äºç´çº¿å¯¹ç§°.
74ã设X~2/A~2+ Y~2/B~2 =1(A>B>0)ä¸ç´çº¿X+Y-1=0交äºPQ,ä¸PQåç´OQ,æ±è¯1/A~2+1/B~2为å®å¼.è¥E(离å¿ç)å±äº[æ ¹3/3,æ ¹2/2],æ±é¿è½´çåå¼èå´ ã
75ï¼æ¤å x^2/25 + y^2/16 = 1 å æ两ç¹: M(2,2) N(3,0) ï¼Pæ¯æ¤åä¸ä»»æä¸ç¹ æ±|PM|+|PN|çæå°å¼ã
76ï¼è®¾æ¤åæ¹ç¨ä¸ºX~2/A~2+ Y~2/B~2 =1(A>B>0)ï¼çè½´çä¸ä¸ªé¡¶ç¹Bä¸ä¸¤ç¦ç¹F1ï¼F2ç»æçä¸è§å½¢çå¨é¿ä¸º4+2æ ¹3ï¼ä¸è§F1BF2为120度ï¼æ±æ¤åæ¹ç¨ã
77ãæ¤åçç¦è·æ¯é¿è½´é¿ï¼çè½´é¿ççæ¯ä¸é¡¹ï¼åæ¤åç离å¿çæ¯å¤å°ï¼
78ã设P为æ¤åæ åæ¹ç¨ä¸ä»»ä¸ç¹ï¼F1ï¼F2åå«ä¸ºå·¦ï¼å³ç¦ç¹ï¼æ±PF1çç»å¯¹å¼ä¸PF2çç»å¯¹å¼çæ大å¼åæå°å¼ã
79ï¼å¨æ¤åä¸ä»¥ç¦ç¹F1F2为ç´å¾ä¸¤ç«¯ç¹çåï¼æ°å¥½è¿çè½´ç两顶ç¹ï¼åæ¤æ¤åç离å¿ççäºå¤å°ï¼
80ï¼Pæ¯æ¤åX~2+2Y~2=16ä¸çå¨ç¹ï¼Fæ¯ä¸ä¸ªç¦ç¹ï¼åPFçæå°å¼æ¯å¤å°ï¼
81ï¼å¨ååå®åM:x~2+y~2-4y-32=0å å,ä¸è¿å®ç¹A(0,-2),æ±å¨ååå¿Pç轨迹ã
82ï¼è¿æ¤å2X~2+Y~2=2çä¸ç¦ç¹çç´çº¿L交æ¤åäºAï¼B两ç¹ï¼æ±ä¸è§å½¢AOBï¼O为åç¹ï¼çé¢ç§¯æ大å¼ï¼
83ï¼å¨Y=Xçå¾è±¡ä¸ï¼ æ¾ä¸ç¹P ï¼Pä¸A(2.0)åä¸(-2.0)çè·ç¦»ä¹å为8 ï¼æ±Påæ ã
84ï¼å¨æ¤åä¸æ±ä¸ç¹ä½¿å®å°æ¤åå¤ç两å®ç¹è·ç¦»åçæ大å¼ãæå°å¼ã
85ï¼è¥æ¤åé¿è½´,çè½´,ç¦è·çé¿åº¦ä¹åçäº8,åé¿åè½´çåå¼èå´æ¯_____,å½é¿åè½´åå¾æå°å¼æ¶,æ¤åç离å¿ççäº_____.
86ï¼è¿æ¤åC:X~2/4+Y~2=1çå³ç¦ç¹,ä½ä¸ç´çº¿l交æ¤åCäºM,Nå°å³å线X=4/æ ¹3çè·ç¦»ä¹åä¸ºæ ¹3,æ±ç´çº¿læ¹ç¨.
87ï¼å·²ç¥A(4,0),B(2,2)æ¯æ¤åx~2/25+y~2/9=1å çç¹,Mæ¯æ¤åä¸çå¨ç¹.æ±|MA|+|MB|çæ大å¼ä¸æå°å¼.
88ï¼å·²ç¥æ¤åä¸ç¹ä¸ºåç¹, ç¦ç¹å¨æ¨ªè½´ä¸ï¼ç¦»å¿çä¸ºæ ¹3/2ï¼ä¸x+y+1=0交äºPãQ,å½OPåç´OQæ¶ï¼æ±æ¤åæ¹ç¨ã
89ï¼æ±ååæ²çº¿X~2-Y~2=8æå ±åç¦ç¹ä¸ç»è¿ç¹Pï¼4ï¼6ï¼çæ¤åçæ¹ç¨ã
90ï¼ä»¥ï¼2ï¼0ï¼ä¸ºç¦ç¹ï¼y轴为å线çæ¤åæå 个ï¼
91ï¼æ¤åX~2/A~2+Y~2/B~2=1ï¼ï¼A>B>0ï¼ç两ç¦ç¹ä¸ºF1ãF2ï¼æç为Kçç´çº¿è¿å³ç¦ç¹F2ï¼ä¸æ¤å交äºAãBï¼ä¸Y轴交äºCï¼B为F2ä¸ç¹ï¼è¥Kçç»å¯¹å¼å°äºçäº2[æ ¹5]/5ï¼æ±æ¤å离å¿çèå´ã
92ãå·²ç¥æ¤åç两个ç¦ç¹åå«æ¯F1(-2æ ¹å·2,0),F2(2æ ¹å·2)é¿è½´é¿ä¸º6,ç´çº¿X-Y+2=0 ä¸æ¤åç¸äº¤äºA,B两ç¹ãæ±: (1)æ¤åçæ åæ¹ç¨ (2)线段ABçé¿åº¦
93ï¼ä¸æ¤åä¸ä¸¤ç¹p,q, opåç´oq,å1/OPæ¹+ 1/OQæ¹æ¯å®å¼ã
94ï¼çº¿æ®µABå®é¿ï¼Cæ¯ABä¸çä¸ä¸ªå®ç¹ï¼ç¸å¯¹ABåºå®ï¼ï¼AB两端ç¹åå«å¨ä¸¤å®ç´çº¿ä¸è¿å¨ï¼æ±Cçè½¨è¿¹ï¼ [æ¯ä¸ªæ¤å]
95ï¼æ¤åå æ¥æ£æ¹å½¢çé¢ç§¯æä¹æ±?
96ï¼æ¤åx^2/a^2+y^2/b^2=1(a>b>0)çå·¦å³ç¦ç¹åå«ä¸ºF1åF2ï¼A1(-a,0)ï¼A2(a,0)ï¼B(0,b)ï¼Pæ¯æ¤åä¸ä¸ç¹ï¼è¥F2å°ç´çº¿ABçè·ç¦»ä¸ºb/æ ¹å·7ï¼æ±æ¤åç离å¿çã
97ï¼æ±ä»¥ï¼Â±4ï¼0ï¼åï¼0ï¼Â±3ï¼ä¸ºé¡¶ç¹çæ¤åçæ åæ¹ç¨ã
98ï¼pæ¯æ¤å(aï¼bï¼0)ä¸å¼äºé¿è½´ç«¯ç¹çä»»ä¸ç¹ï¼F1ãF2æ¯æ¤åç两个ç¦ç¹ï¼è¥â PF1F2=α,â PF2F1=βï¼æ±è¯ï¼
æ¤åç离å¿çe=cos0.5ï¼Î±+βï¼/cos0.5ï¼Î±ï¼Î²ï¼
99ï¼ç¹Aï¼Båå«æ¯æ¤åXï¼¾ï¼36+Yï¼¾ï¼20ï¼1é¿è½´çå·¦ï¼å³ï¼ç¹Fæ¯æ¤åçå³ç¦ç¹ï¼ç¹På¨æ¤åä¸ï¼ä¸ä½äºXè½´ä¸æ¹ï¼PAâ¥PB
ï¼1ï¼æ±Pç¹çåæ ï¼
ï¼2ï¼è®¾Mæ¯æ¤åé¿è½´ABä¸çä¸ç¹ï¼Må°ç´çº¿APçè·ç¦»çäºï¼MBï¼ï¼æ±æ¤åä¸çç¹å°ç¹Mçè·ç¦»dçæå°å¼ï¼
100ï¼å·²ç¥ç¹Aï¼ï¼2ï¼0ï¼ï¼Bï¼3ï¼0ï¼ï¼å¨ç¹Pï¼x,yï¼æ»¡è¶³åéçç¹ç§¯PA*PBï¼x~2ï¼åç¹ç轨迹æ¯AåBæ¤åCåæ²çº¿Dæç©çº¿ã
101ï¼å·²ç¥M为æ¤åä¸ä¸ç¹ï¼F1F2æ¯ä¸¤ç¦ç¹ï¼ä¸â MF1F2=2αï¼â MF2F1=α(αâ 0)ï¼åæ¤åç离å¿çæ¯( )ã
102ï¼P为æ¤å x^2/25+y^/16=1ä¸ä¸ç¹ï¼F1ãF2为左å³ç¦ç¹ãï¼1ï¼è¥PF1çä¸ç¹ä¸ºMï¼æ±è¯â£MOâ£=5â1/2â£PF1â£ãï¼2ï¼è¥â F1PF2=60°ï¼æ±â£PF1â£*â£PF2â£çå¼ãï¼3ï¼æ±â£PF1â£*â£PF2â£çæå¼
103ï¼ææ¤åX^2/6+Y^2/2=1,ç¹N(3,0),è¿Nçç´çº¿ä¸åä½åX^2+Y^2=1æ¤å交äºP,Q,R,S,ä¸|PQ|=|RS|,æ±æ¯å¦åå¨,åå¨å³æ±åºè¯¥ç´çº¿ã
104ï¼è®¾ç´çº¿Y=2x+1ä¸æ¤åX~2/4+Y~2=1ç¸äº¤äºAB两ç¹ï¼æ±AB两ç¹Må°åæ åç¹çè·ç¦»ã
105ï¼å·²ç¥æ¤åx2+2y2=98åç¹p(0,5),æ±æ¤åä¸çç¹å°pçè·ç¦»çæ大å¼åæå°å¼
106ï¼å·²ç¥æ¤åx^2/a^2+y^2/b^2=1(a>b>0)ç离å¿çæ¯[æ ¹6]/3ï¼Fæ¯å ¶å·¦ç¦ç¹ï¼è¥ç´çº¿x-æ ¹6=0ä¸æ¤å交ä¸AB两ç¹ï¼ä¸åéFA*åéFB=-1,æ±è¯¥æ¤åæ¹ç¨ï¼
107ï¼å¨æ¤åx~2+y~2/a~2=1(0<a<1)ä¸,è·é¡¶ç¹A(0,a)è·ç¦»æ大çç¹æ°å¥½æ¯å¦ä¸é¡¶ç¹A'(0,-a),æ±å®æ°açåå¼èå´ã
108ï¼å·²ç¥ç´çº¿y=kx+2åæ¤å2x^2+3y^2=6æä¸¤ä¸ªå ¬å ±ç¹ï¼åkçåå¼èå´æ¯ï¼ ï¼ã
109ï¼æ¤åçä¸å¿å¨åç¹,ç¦ç¹å¨Xè½´ä¸,并è¿ç¹M1(6,4)åM2(8,-3),æ±æ¤åçæ åæ¹ç¨.
110ï¼ä¸å¨ç¹å°å®ç¹A(3,0)çè·ç¦»åå®å°ç´çº¿X=12çè·ç¦»çæ¯ä¸º1/2,æ±å¨ç¹ç轨迹æ¹ç¨.
111ï¼å¨å¹³é¢ç´è§åæ ç³»ä¸ï¼è¥æ¹ç¨m(x^2+y^2+2y+1)=(x-2y+3)^2表示çæ²çº¿ä¸ºæ¤åï¼åå®æ°mçåå¼èå´æ¯ï¼ ï¼ã
112ï¼ä¸ä¸ªæ¤åçé¿è½´é¿æ¯çè½´é¿ç两å ï¼æ±è¿æ¤å离å¿çã
113ï¼åæ²çº¿çä¸å¿å¨åæ åç¹ï¼ 离å¿ççäº2 ï¼ä¸ä¸ªç¦ç¹åæ 为(2,0)ï¼ æ±åæ²çº¿æ¹ç¨ã
114ï¼å·²ç¥æ¤åa^2*x^2-0.5a*y^2=1çä¸ä¸ªç¦ç¹åæ æ¯(-2,0)ï¼æ±açå¼ã
115ãç»è¿æ¤åx^2/4+y^2/3=1çä¸ä¸ªç¦ç¹F1çç´çº¿äº¤æ¤åäºAåB两ç¹,F2æ¯å¦ä¸ä¸ªç¦ç¹,åä¸è§å½¢ABF2çå¨é¿æ¯ï¼ ï¼ã
116ï¼æ¤åx~2/a~2+y~2=1(a>1)çä¸ä¸ªç¦ç¹ä¸ºF,ç¹På¨æ¤åä¸,ä¸/OP/=/OF/(O为åæ åç¹),åâ³OPFçé¢ç§¯Sæ¯ï¼ ï¼ã
117ï¼ä¸æ¤åx^2/4+y^2=1å ±ç¦ç¹ä¸è¿ç¹Q(2,1)çåæ²çº¿æ¹ç¨æ¯______ã
118ï¼ç´çº¿y=kx-1åæ¤åx~2/4 + y~2/(âa)~2=1 ç¸å ï¼æ±kåaçåå¼èå´ã
119ï¼æ¤åx~2/25 + y~2/9=1ä¸æ3个ç¹Aï¼x1ï¼y1)ï¼ B(4ï¼9/5 )ï¼ C(x2ï¼y2) å®ä»¬åå³ç¦ç¹ï¼4,0)è·ç¦»æçå·®æ°å ï¼æ±X1+X2çå¼ã
120ï¼è¥ç¹A(0,7)ï¼B(0,-7)ï¼C(æ ¹2ï¼2ï¼ï¼ä»¥C为ä¸ç¦ç¹ä½è¿Aï¼Bçæ¤åï¼æ±å¦ä¸ç¦ç¹ç轨迹æ¹ç¨ã
121ï¼ä»¥ï¼ï¼1ï¼2ï¼ï¼ï¼7ï¼2ï¼ä¸ºç¦ç¹ï¼çè½´é¿ä¸º6çæ¤åæ¹ç¨æ¯ï¼ ï¼ã
122ï¼å·²ç¥F1ãF2æ¯æ¤åx~2/a~2+y~2/(10-a)~2=1(5<a<10)ç两个ç¦ç¹ï¼Bæ¯çè½´çä¸ä¸ªç«¯ç¹ï¼åâ³F1BF2çé¢ç§¯çæ大å¼æ¯å¤å°ï¼
123ï¼è®¾æç为K1çç´çº¿L交æ¤åX~2ï¼2ï¼Y~2ï¼1äºAï¼B两ç¹ï¼ç¹M为弦ABçä¸ç¹ï¼ç´çº¿OMçæç为K2ï¼O为åæ åç¹ï¼å设K1ï¼K2é½åå¨ï¼ æ±K1*K2çå¼ã
124ï¼è®¾æ¤åx~2/a~2+y~2/b~2=1ï¼éè¿æ¤åå¤ä¸ç¹(m,n)æ±å°æ¤åçå¾æè¿åæè¿ç¹?
125ï¼ä¾å¦,åæ²çº¿ x^2/4-y^2/12=1 ï¼å®ç两个顶ç¹çåæ æ¯(-2.0)ä¸(2.0)ï¼é£ä¹å¤æå¨åæ²çº¿çå·¦æ¯ä¸å³åªåºè¯¥è®©Xåå«æ»¡è¶³ä»ä¹æ¡ä»¶å?
126ï¼å·²ç¥åæ²çº¿y=k/xè¿ç¹Aï¼2ï¼3ï¼ï¼ï¼1ï¼è¥Aå ³äºç´çº¿y=xç对称ç¹ä¸ºBï¼è¯å¤æç¹Bæ¯å¦å¨åæ²çº¿y=k/xä¸ï¼å¹¶è¯´æçç±ï¼ï¼2ï¼æ±ä¸è§å½¢OABçé¢ç§¯
127ï¼ä¸å¿å¨åç¹,ä¸ä¸ªç¦ç¹ä¸ºF(1,0)çåæ²çº¿,å ¶å®é¿è½´é¿ä¸èè½´é¿ä¹æ¯ä¸ºm,æ±æ¤åæ²çº¿çæ åæ¹ç¨ã
128ï¼å·²ç¥åæ²çº¿ç离å¿ç为2,åå®ç两æ¡æ¸è¿çº¿ç夹è§ä¸º_____ã
129ï¼åæ²çº¿x~2/16-y~2/9=1ï¼å ¶ä¸æä¸ç¹Pï¼è§F1PF2çäº60度ï¼æ±ä¸è§å½¢F1PF2çé¢ç§¯ã
130ï¼åæ²çº¿X~2/a~2âY~2/b~2=1(a>1,b>0)çç¦è·2C,ç´çº¿Lè¿(a,0)(b,0)ä¸(1,0)å°ç´çº¿Lçè·ç¦»ä¸ç¹(-1,0)å°Lè·ç¦»ä¹åS>=4C/5,æ±åæ²çº¿ç离å¿çeçåå¼èå´?
131ï¼è®¾ç¹På°ç¹Mï¼-1ï¼0ï¼ãNï¼1ï¼0ï¼è·ç¦»ä¹å·®ä¸º2m,å°Xè½´ãYè½´è·ç¦»ä¹æ¯ä¸º2ãæ±mçåå¼èå´ã
132ï¼ä¸ä¸ªæ£ä¸è§å½¢çä¸ä¸ªé¡¶ç¹åå¨åæ²çº¿x^2-ay^2=1çå³æ¯ä¸,å ¶ä¸ä¸ä¸ªé¡¶ç¹ä¸åæ²çº¿çå³é¡¶ç¹éå,åå®æ°açåå¼èå´?
133ï¼è®¾F1 ï¼F2æ¯åæ²çº¿X~2/4-Y~2=1 ç两个ç¦ç¹ï¼ç¹På¨åæ²çº¿ä¸ï¼ä¸PF1åç´PF2ï¼åPF1*PF2çäºï¼ ï¼ã [çæ¡ï¼2]
134ï¼ç´çº¿Yï¼aXï¼1ï¼0ä¸åæ²çº¿3Xï¼¾2ï¼Yï¼¾2=1ç¸äº¤äºAï¼B两ç¹ï¼ï¼1ï¼å½a为ä½å¼æ¶ï¼Aï¼Bå¨åæ²çº¿çåä¸æ¯ä¸ï¼å½a为ä½å¼æ¶ï¼Aï¼Båå«å¨åæ²çº¿ç两æ¯ä¸ï¼ï¼2ï¼å½a为ä½å¼æ¶ï¼ä»¥AB为ç´å¾ä¸ååè¿åæ åç¹ï¼
135ï¼åæ²çº¿x²-y²=a²(a>0)çå·¦ï¼å³é¡¶ç¹åå«ä¸ºAï¼Bï¼ç´çº¿låç´äºå®è½´æå¨çç´çº¿ä¸ä¸åæ²çº¿äº¤äºPï¼Q两ç¹ï¼æ±è¯ï¼â PAQ+â PBQ=180°ã
136ï¼å·²ç¥åæ²çº¿mï¼x^2/a^2-y^2/b^2=1(a>0,b>0)ï¼ç¦»å¿çe=2ï¼çº¿æ®µABçåç´å¹³å线为x-y-2=0ï¼ä¸|AB|=æ ¹46
ï¼1ï¼ æ±åæ²çº¿ç»è¿äºï¼å象éçæ¸è¿çº¿çå¾æè§
ï¼2ï¼ æ±çº¿æ®µABä¸ç¹Cçåæ
ï¼3ï¼ æ±ç´çº¿ABçæ¹ç¨
ï¼4ï¼ æ±åæ²çº¿mçæ¹ç¨
137ï¼å ³äºxy=1çé®é¢ï¼ä¸å¤ªæç½ ï¼æ¤ååæ²çº¿ç离å¿çåæ¯ä¼ï¼è¿ä¸ªç¦»å¿çæ¯ä»£è¡¨çæ¯ä»ä¹æä¹å¢ï¼
138ï¼è¯·é®ä¸ä¸ï¼å¨åæ²çº¿ä¸è¿ä¸ç¦ä¸åæ²çº¿ç¸äº¤çç´çº¿ï¼Kä¸çäº0ï¼ï¼éå¾é¿æ¯æççåï¼
139ï¼è®¾ç´çº¿Lçæ¹ç¨ä¸ºy=kx-1,çè½´åæ²çº¿Cçä¸å¿å¨åç¹ï¼å³ç¦ç¹åæ 为ï¼æ ¹2ï¼0ï¼ï¼ç´çº¿Lä¸åæ²çº¿å³æ¯äº¤äºä¸åç¹Aï¼Bï¼è®¾å¼¦ABçä¸ç¹åæ 为Mï¼Qç¹åæ 为ï¼-1ï¼0ï¼ï¼æ±ç´çº¿QMå¨yè½´ä¸çæªè·çåå¼èå´ã
140ï¼è®¾Pæ¯åæ²çº¿X~2/3-Y~2=1çå³æ¯ä¸ä¸ä¸ªå¨ç¹ï¼Fæ¯åæ²çº¿çå³ç¦ç¹ï¼å·²ç¥Aç¹çåæ æ¯(3,1)ï¼å|PA|+|PF|çæå°å¼æ¯_______ã
141ï¼Fæ¯åæ²çº¿X~2/16-Y~2/9=1å³ç¦ç¹ï¼Mæ¯åæ²çº¿å³æ¯ä¸ä¸å¨ç¹ï¼å®ç¹Açåæ 为(5,4)ï¼å4|MF|-5|MA|çæ大å¼æ¯______ã
142ï¼å·²ç¥çè½´åæ²çº¿ç»è¿ç¹ï¼-3ï¼2ï¼ä¸å¯¹ç§°è½´é½å¨åæ è½´ä¸ï¼æ±å®çæ¹ç¨ã
143ï¼å·²ç¥åæ²çº¿(x-h)(y-k)=a(aä¸ä¸º0)çæ°´å¹³æ¸è¿çº¿y=k,ç«ç´æ¸è¿çº¿ä¸ºx=h,ä¸å¿ä¸ºï¼h,k),è¥åæ²çº¿y=x/(x-1) çç¹å°å®çæ°´å¹³æ¸è¿çº¿ï¼ç«ç´æ¸è¿çº¿ï¼ä¸å¿çè·ç¦»åå«æ¯d1,d2,d3.åd1+d2+d3çæå°è·ç¦»ä¸ºï¼ ï¼ã
A4ãããB2ï¼æ ¹2ããC3ï¼æ ¹2ããD3
144ï¼éè¿ä¸ç¹(1,3)ä½ä¸æ¡ç´çº¿,ååæ²çº¿y*y=-16xäºAB两ç¹.æ±åç¹åæ .
145ï¼ç´çº¿y-ax-1=0 ååæ²çº¿3x^2-y^2=1ç¸äº¤äºA ï¼Bä¸¤ç¹ a为ä½å¼æ¶ã以AB为ç´å¾çåç»è¿åç¹ï¼
146ãåæ²çº¿ x^2-y^2=1 ï¼ç´çº¿l ï¼y=kx+m (kä¸ä¸º0)ä¸åæ²çº¿äº¤äºA,B.æD(0,-1),ä¸æ|AD|=|BD|,æ±mèå´ã
147ï¼å·²ç¥ç´çº¿ï¼l1:5x+3y=0ål2:5x-3y=0ï¼å¦æ以ç´çº¿l1ål2为æ¸è¿çº¿çåæ²çº¿ç»è¿ç¹Mï¼1ï¼3ï¼ï¼æ±æ¤åæ²çº¿çæ åæ¹ç¨ã
148ï¼ç»è¿ç´çº¿L:x+y-2=0ä¸ä¸ç¹mä¸ä»¥åæ²çº¿X~2/12-Y~2/4=1çç¦ç¹ä¸ºç¦ç¹ä½åæ²çº¿ï¼å½må¨ä½å¤æ¶ï¼æä½åæ²çº¿å®è½´é¿æé¿ï¼å¹¶æ±åºå ·ææé¿å®è½´çåæ²çº¿æ¹ç¨ã
149ï¼ä¸¤å®ç¹ABè·ç¦»ä¸º6,å¨ç¹M满足è§MBA=2è§MAB,æ±å¨ç¹Mç轨迹æ¹ç¨.
150ï¼å·²ç¥åæ²çº¿çå®è½´2aï¼8ï¼ç´çº¿MNè¿ç¦ç¹F1交åæ²çº¿äºMï¼Nï¼ MNï¼7ï¼æ±ä¸è§å½¢MNF2ï¼F2为å¦ä¸ç¦ç¹)çå¨é¿ã
151ï¼è¿ç¹P(4,4)ä¸åæ²çº¿x^2/16-y^2/19=1åªæä¸ä¸ªå ¬å ±ç¹çç´çº¿æå æ¡?
152ï¼å·²ç¥åæ²çº¿ä¸¤æ¡æ¸è¿çº¿æ¹ç¨ä¸ºY=±2X,ç´çº¿Y=X+3被åæ²çº¿æªå¾å¼¦é¿ä¸º8,ååæ²çº¿æ¹ç¨ä¸º?
153ï¼ç´çº¿y=kx+m(kä¸çäº0,mä¸çäº0)ä¸åæ²çº¿x~2/3 ây~2 =1交äºä¸å两ç¹CãD åCãD两ç¹é½å¨ä»¥A(0,-1)为åå¿çåä¸ä¸ªåä¸,æ±mçåå¼èå´.
154ï¼å·²ç¥åæ²çº¿çä¸å¿å¨åæ åç¹,å³ç¦ç¹F(2,0),以F为åå¿,OF为åå¾ä½åä¸åæ²çº¿çä¸æ¡æ¸è¿çº¿äº¤ä¸Oï¼A两ç¹ï¼è¥2â¤OAâ¤2â2
ï¼1ï¼æ±åæ²çº¿ç离å¿çeçåå¼èå´
ï¼2ï¼è¿Fçç´çº¿ä¸åæ²çº¿çå³æ¯äº¤ä¸MãN两ç¹ä¸MF=2FNï¼æ³¨ï¼MFä¸FN为åéï¼ï¼æ±ç´çº¿MNçæçæå°æ¶åæ²çº¿çæ¹ç¨ã
155ï¼å·²ç¥åæ²çº¿Cç两æ¡æ¸è¿çº¿è¿åç¹,ä¸ä¸å ¶å³é¡¶ç¹A2(æ ¹å·2,0)为åå¿,1为åå¾çåé½ç¸å.è¥è®¾æ²çº¿Cç左顶ç¹ä¸ºA1,Pä¸ºå ¶å³æ¯ä¸ä»»ä¸ç¹(ä¸A2ä¸éå)è¯å¤æç´çº¿A1Pä¸A2Pçç¡®å¾æè§ä¹é´çå ³ç³»ã
156ï¼è®¾ç¹Pæ¯åæ²çº¿X~2/16-Y~2/9=1å³æ¯ä¸ä¸ç¹ï¼Fæ¯è¯¥åæ²çº¿çå³ç¦ç¹ï¼Mæ¯PFçä¸ç¹,O为åæ åç¹ï¼ä¸|OM|=6,åç¹På°è¯¥åæ²çº¿å³å线çè·ç¦»ä¸º( )ã
A.5 B.16/5 C.15 D.48/5
157ï¼è¿ç¹N(0,-2)ä½ç´çº¿l交åæ²çº¿Cï¼x~2ï¼y~2ï¼1äºAï¼B以OAï¼OB为é»è¾¹åå¹³è¡å边形OAPBï¼æ±ç¹Pç轨迹æ¹ç¨ï¼
158ï¼å·²ç¥MåN两ç¹å ³äºY轴对称,ä¸ç¹Må¨åæ²çº¿Y=1/2X,ç¹Nå¨Y=X+3ä¸,设ç¹Mçåæ 为(A,B),æ±æ ¹å·[A~2+B~2]çå¼ã
159ï¼åæ²çº¿çä¸å¿å¨åæ åç¹,离å¿ççäº2,ä¸ä¸ªç¦ç¹çåæ 为(2,0),åæ¤åæ²çº¿çæ¹ç¨æ¯ä»ä¹?
160ï¼åæ²çº¿y=2/xçç¦ç¹æ¯å¤å°ï¼
161ï¼å¨åæ²çº¿x^2-y^2=1çå³æ¯ä¸çä¸ç¹P(a,b)å°ç´çº¿y=xçè·ç¦»ä¸ºæ ¹2,æ±aåbçå¼ã
162ãå·²ç¥ä¸è§å½¢ç两个顶ç¹b(-5,0),C(5,0)è¾¹AB,ACæå¨ç´çº¿æçä¹ç§¯ä¸º1/7,æ±ç¬¬ä¸ä¸ªé¡¶ç¹Aç轨迹æ¹ç¨ã
163ï¼æ±ç»è¿å®ç¹Mï¼-3ï¼2ï¼ï¼ä¸ä»¥ç´çº¿X=0为左å线ï¼ç¦»å¿çe=2çåæ²çº¿å³ç¦ç¹ç轨迹æ¹ç¨ã
164ï¼å设ä¸ä¸ªæ¤åCï¼x^2/a^2+y^2/b^2=1(a>b>0)çå·¦å³ç¦ç¹åå«æ¯F1åF2.è¿å³ç¦ç¹F2ä¸xè½´åç´çç´çº¿lä¸æ¤åCç¸äº¤,å ¶ä¸ä¸ä¸ªç¦ç¹ä¸ºM(æ ¹2,1)
ï¼1ï¼ æ±æ¤åCçæ¹ç¨
ï¼2ï¼ è¥p为æ¤åCä¸ä¸ç¹,PF1åç´PF2,æ±ä¸è§å½¢F1PF2çé¢ç§¯.
165ï¼å¨ç´è§åæ ç³»ä¸ï¼ç´çº¿y=x+mä¸åæ²çº¿y=m/xå¨ç¬¬ä¸è±¡é交äºç¹Aï¼ä¸x轴交äºç¹Cï¼ABåç´xè½´ï¼å足为Bï¼ä¸ä¸è§å½¢AOBçé¢ç§¯çäº1ã
ï¼1ï¼æ±må¾å¼ï¼2ï¼æ±ä¸è§å½¢ABCçé¢ç§¯
166ï¼ä»¥ç¥F1ï¼F2åå«æ¯åæ²çº¿x^2/a^2-y^2/b^2=1(a>0,b>0)çå·¦å³ç¦ç¹ï¼P为åæ²çº¿å·¦æ¯ä¸ä»»æä¸ç¹ï¼è¥|PF2|^2/|PF1|çæå°å¼ä¸º8a,å该åæ²çº¿ç¦»å¿çeçåå¼èå´æ¯? çæ¡æ¯ï¼ï¼1ï¼3ã
167ï¼çè½´åæ²çº¿ï¼ ç¦ç¹F1ï¼-2ï¼2ï¼ï¼F2ï¼4ï¼-4ï¼ï¼æ±åæ²çº¿ï¼
168ï¼å·²ç¥åæ²çº¿X^2/a^2-Y^2/b^2=1(a>0,b>0)ç左顶ç¹ä¸ºA(-1,0),è¿ç¹Aä½ä¸¤æ¡ç´çº¿åå«äº¤åæ²çº¿çå³æ¯äºB(X1,Y1)ãCï¼X2ï¼Y2ï¼ä¸¤ç¹ï¼ä¸ä¸è§å½¢ABC为æ£ä¸è§å½¢ã
ï¼1ï¼è¯æï¼BãC两ç¹å ³äºX轴对称
ï¼2ï¼è®¾X1>2ï¼æ±bçåå¼èå´
169ãx^2+xy-6y^2-20y-20x+k=0 表示两æ¡ç´çº¿,æ±è¿ä¸¤æ¡ç´çº¿ã
温馨提示:答案为网友推荐,仅供参考
第1个回答 2012-02-20
我的是WORD文档的,不知道怎么传上来,要的话Q我。1259014310.