已知点(2,3)在双曲线C:x²/a²-y²/b²=1(a>0,b>0)上,C的焦距为4,则它的离心率为
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![已知点(2,3)在双曲线C:x²/a²-y²/b²=1(a>0,b>0)上,C的焦距为4,则它的离心率为](/uploads/image/z/2541040-16-0.jpg?t=%E5%B7%B2%E7%9F%A5%E7%82%B9%EF%BC%882%2C3%EF%BC%89%E5%9C%A8%E5%8F%8C%E6%9B%B2%E7%BA%BFC%3Ax%26%23178%3B%2Fa%26%23178%3B-y%26%23178%3B%2Fb%26%23178%3B%3D1%28a%EF%BC%9E0%2Cb%EF%BC%9E0%29%E4%B8%8A%2CC%E7%9A%84%E7%84%A6%E8%B7%9D%E4%B8%BA4%2C%E5%88%99%E5%AE%83%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87%E4%B8%BA)
已知点(2,3)在双曲线C:x²/a²-y²/b²=1(a>0,b>0)上,C的焦距为4,则它的离心率为
已知点(2,3)在双曲线C:x²/a²-y²/b²=1(a>0,b>0)上,C的焦距为4,则它的离心率为
已知点(2,3)在双曲线C:x²/a²-y²/b²=1(a>0,b>0)上,C的焦距为4,则它的离心率为
∵ 焦距2c为4
∴ c=2
双曲线C:x²/a²-y²/b²=1(a>0,b>0)
∴ 焦点在x轴上
∴ 焦点F1(-2,0),F2(2,0)
已知点M(2,3)在双曲线上,
则|MF1|=√[(2+2)²+(3-0)²]=5
|MF2|=√[(2-2)²+(3-0)²]=3
∴ 2a=|MF1|-|MF2|=2
∴ a=1
∴ 离心率e=c/a=2