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.
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