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(x0, y0) = (−(c2+c2), 0)
å ¶ä¸ï¼c1åc2åå«æ¯æ¤åçé¿åè½´åçåè½´ã
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x=rcosθâ¢
y=rsinθâ£
å ¶ä¸ï¼(x, y)æ¯æ¤åä¸ä»»æä¸ç¹çåæ ï¼ræ¯æ¤åä¸çç¹å°æ¤åä¸å¿çè·ç¦»ï¼Î¸æ¯æ¤åçæ转è§åº¦ã
æ ¹æ®æ¤åçå®ä¹ï¼æ¨å¯¼åºæ¤åçæ åæ¹ç¨ãå°â¡å¼ä¸çxåyç¨â¢å¼åâ£å¼ä»£æ¿ï¼å¾å°ä»¥ä¸æ¹ç¨ï¼
(rcosθ)2/a2+(rsinθ)2/b2=1â¤
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r2=(cos2θ/a2)+(sin2θ/b2)â¥
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abcos2θ+(acos2θ+bsin2θ)c=(a+c)2â§
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ab−absin2θ+(acos2θ+bsin2θ)c=(a+c)2â¨
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ab−absin2θ+acos2θ(a+c)+b(1−cos2θ)(a+c)=(a+c)2â©
å°â©å¼ä¸çsin2θç¨1-cos2θ代æ¿ï¼å¾å°ä»¥ä¸æ¹ç¨ï¼
ab−ab(1−cos2θ)+acos2θ(a+c)+b(1−cos2θ)(a+c)=(a+c)2⑪
代入椭圆方程x^2/4+y^2/3=1,得
3x^2+4(x^2+2x+1)=12,
整理得7x^2+8x-8=0,
△=64+4*7*8=8*36,
设A(x1,y1),B(x2,y2),则|x1-x2|=√△/7,
所以|AB|=|x1-x2|√2=24/7.