Question

高考数学问题:以椭圆x^2/18+y^2/12=1的顶点为焦点

Answer 1

1

椭圆x^2/18+y^2/12=1的长轴顶点为(3√2,0)和(-3√2,0);

焦点为(-√6,0)和(√6,0).

则以椭圆x^2/18+y^2/12=1的顶点为焦点,焦点为顶点的双曲线

半焦距是c=3√2;实半轴长√6;虚半轴长√[(3√2)^2-(√6)^2]=2√3;

则双曲线方程是

x^2/6-y^2/12=1.

2

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