双曲线与椭圆X²/27+Y²/36=1有相同焦点,且经过点(√15,4),求其方程.
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![双曲线与椭圆X²/27+Y²/36=1有相同焦点,且经过点(√15,4),求其方程.](/uploads/image/z/2556073-1-3.jpg?t=%E5%8F%8C%E6%9B%B2%E7%BA%BF%E4%B8%8E%E6%A4%AD%E5%9C%86X%26%23178%3B%2F27%EF%BC%8BY%26%23178%3B%2F36%3D1%E6%9C%89%E7%9B%B8%E5%90%8C%E7%84%A6%E7%82%B9%2C%E4%B8%94%E7%BB%8F%E8%BF%87%E7%82%B9%28%E2%88%9A15%2C4%29%2C%E6%B1%82%E5%85%B6%E6%96%B9%E7%A8%8B.)
双曲线与椭圆X²/27+Y²/36=1有相同焦点,且经过点(√15,4),求其方程.
双曲线与椭圆X²/27+Y²/36=1有相同焦点,且经过点(√15,4),求其方程.
双曲线与椭圆X²/27+Y²/36=1有相同焦点,且经过点(√15,4),求其方程.
椭圆焦点在Y轴上:a^2=36,b^2=27,则c^2=36-27=9
即焦点坐标是(0,4)和(0,-4)
设双曲线方程是y^2/a^2-x^2/b^2=1.
故a^2+b^2=c^2=9.(1)
坐标代入得:16/a^2-15/b^2=1.(2)
(1)(2)解得:a^2=36或4.则b^2=-27或5.
负的舍去,得a^2=4,b^2=5
所以,方程是y^2/4-x^2/5=1