如题所述
3ã
ä¸ä¸¤åæ è½´é½ç¸åï¼åå¿(a,a)æè (a,-a)
(1) åå¿ä¸º(a,a)æ¶
设åæ¹ç¨ï¼(x-a)^2+(y-a)^2=r^2
ä¸ç´çº¿3x+4y-4=0ç¸åï¼åå¿å°ç´çº¿çè·ç¦»d=r
r^2=d^2
=|3a+4a-4|^2/[â(3^2+4^2)]^2
=(7a-4)^2/25
åæ¹ç¨ï¼(x-a)^2+(y-a)^2=(7a-4)^2/25
è¿(a,0)
(a-a)^2+(0-a)^2=(7a-4)^2/25
25a^2=49a^2-56a+16
24a^2-56a+16=0
8(3a-1)(a-2)=0
a=1/3
r^2=(7/3-4)^2/25=1/9
åæ¹ç¨ï¼(x-1/3)^2+(y-1/3)^2=1/9
æè a=2
r^2=(7Ã2-4)^2/25=4
åæ¹ç¨ï¼(x-2)^2+(y-2)^2=4
(2) å½åå¿ä¸º(a,-a)æ¶
åæ¹ç¨ï¼(x-a)^2+(y+a)^2=r^2
ä¸ç´çº¿3x+4y-4=0ç¸åï¼åå¿å°ç´çº¿çè·ç¦»ï¼d=r
r^2=d^2
=|3a-4a-4|^2/[â(3^2+4^2)]^2
=(-a-4)^2/25
=(a+4)^2/25
(x-a)^2+(y+a)^2=(a+4)^2/25
è¿(a,0)
(a-a)^2+(0+a)^2=(a+4)^2/25
25a^2=a^2+8a+16
24a^2-8a-16=0
8(3a+2)(a-1)=0
a=-2/3
r^2=(-2/3+4)^2/25
=4/9
åæ¹ç¨ï¼(x+2/3)^2+(y-2/3)^2=4/9
æè a=1
r^2=(1+4)^2/25=1
åæ¹ç¨ï¼(x-1)^2+(y+1)^2=1
综述ï¼åæ¹ç¨å¦ä¸ï¼
(x-1/3)^2+(y-1/3)^2=1/9
(x-2)^2+(y-2)^2=4
(x+2/3)^2+(y-2/3)^2=4/9
(x-1)^2+(y+1)^2=1
ä¸ä¸¤åæ è½´é½ç¸åï¼åå¿(a,a)æè (a,-a)
(1) åå¿ä¸º(a,a)æ¶
设åæ¹ç¨ï¼(x-a)^2+(y-a)^2=r^2
ä¸ç´çº¿3x+4y-4=0ç¸åï¼åå¿å°ç´çº¿çè·ç¦»d=r
r^2=d^2
=|3a+4a-4|^2/[â(3^2+4^2)]^2
=(7a-4)^2/25
åæ¹ç¨ï¼(x-a)^2+(y-a)^2=(7a-4)^2/25
è¿(a,0)
(a-a)^2+(0-a)^2=(7a-4)^2/25
25a^2=49a^2-56a+16
24a^2-56a+16=0
8(3a-1)(a-2)=0
a=1/3
r^2=(7/3-4)^2/25=1/9
åæ¹ç¨ï¼(x-1/3)^2+(y-1/3)^2=1/9
æè a=2
r^2=(7Ã2-4)^2/25=4
åæ¹ç¨ï¼(x-2)^2+(y-2)^2=4
(2) å½åå¿ä¸º(a,-a)æ¶
åæ¹ç¨ï¼(x-a)^2+(y+a)^2=r^2
ä¸ç´çº¿3x+4y-4=0ç¸åï¼åå¿å°ç´çº¿çè·ç¦»ï¼d=r
r^2=d^2
=|3a-4a-4|^2/[â(3^2+4^2)]^2
=(-a-4)^2/25
=(a+4)^2/25
(x-a)^2+(y+a)^2=(a+4)^2/25
è¿(a,0)
(a-a)^2+(0+a)^2=(a+4)^2/25
25a^2=a^2+8a+16
24a^2-8a-16=0
8(3a+2)(a-1)=0
a=-2/3
r^2=(-2/3+4)^2/25
=4/9
åæ¹ç¨ï¼(x+2/3)^2+(y-2/3)^2=4/9
æè a=1
r^2=(1+4)^2/25=1
åæ¹ç¨ï¼(x-1)^2+(y+1)^2=1
综述ï¼åæ¹ç¨å¦ä¸ï¼
(x-1/3)^2+(y-1/3)^2=1/9
(x-2)^2+(y-2)^2=4
(x+2/3)^2+(y-2/3)^2=4/9
(x-1)^2+(y+1)^2=1
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第1个回答 2015-04-23
设圆心(x,y),点到直线距离
|(3 x + 4 y - 4)/5|=|x|,
|x|=|y|,
解得:
y=-1,x=1
y=1/3,x=1/3
y=2/3,x=-2/3
y=2,x=2
半径r=|x|=|y|,
圆的方程为:(x-1)^2+(y+1)^2=1
(x-1/3)^2;+(y-1/3)^2=1/9
(x+2/3)^2+(y-2/3)^2=4/9
(x-2)^2+(y-2)^2=4
第2个回答 2015-04-22
根据已知圆与两轴均相切,可得圆的圆心在x=y直线上。追答
所以设圆心为(x,x)
圆心到题目中直线的距离等于x。
第3个回答 2015-04-22
看不清,哪一题,发个特写追答
看不清,哪一题,发个特写
追问求与两坐标轴及直线3x+4y-4=0都相切的圆的方程