求以椭圆x2/9+y2/5=1的焦点为顶点,以椭圆的顶点为焦点的双曲线方程
求以椭圆x^2/9+y^2/5=1的焦点为顶点,以椭圆的顶点为焦点的双曲线方程
人气:302 ℃ 时间:2019-10-19 21:52:02
解答
1).椭圆中,a^2=9,b^2=5,c^2=a^2-b^2=9-5=4,c=±2.顶点(±3,0),焦点(±2,0).2).双曲线中,顶点(±2,0),焦点(±3,0),3-2=1,故原型为顶点(0,0),焦点(±1,0),y^2=±41x,沿横轴远离原点平移两个单位,即得y^2=±41(x-2)
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