Question

一椭圆与一双曲线有公共焦点,且离心率之和为2,已知椭圆方程为25x^2+9y^2=1,求双曲

Answer 1

设椭圆的离心率为e1,双曲线e2。由题可知c位于y轴上，则a^2=1/9，b^2=1/25。所以c=4/15。e1=c/a=4/5。又因为e1+e2=2，所以e2=6/5。且两个曲线有公共焦点，所以双曲线的A^2=4/81，B^2=44/2025。双曲线x^2/B^2-y^2/A^2=1。

Answer 2

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追问

答案是很複雜的~老師說過..

追答

那就
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