椭圆x²/9+y²/4=1上点P到其右焦点的距离是长轴两端点到右焦点的距离的等差中项,求P点坐标.
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![椭圆x²/9+y²/4=1上点P到其右焦点的距离是长轴两端点到右焦点的距离的等差中项,求P点坐标.](/uploads/image/z/6854847-15-7.jpg?t=%E6%A4%AD%E5%9C%86x%26%23178%3B%2F9%2By%26%23178%3B%2F4%3D1%E4%B8%8A%E7%82%B9P%E5%88%B0%E5%85%B6%E5%8F%B3%E7%84%A6%E7%82%B9%E7%9A%84%E8%B7%9D%E7%A6%BB%E6%98%AF%E9%95%BF%E8%BD%B4%E4%B8%A4%E7%AB%AF%E7%82%B9%E5%88%B0%E5%8F%B3%E7%84%A6%E7%82%B9%E7%9A%84%E8%B7%9D%E7%A6%BB%E7%9A%84%E7%AD%89%E5%B7%AE%E4%B8%AD%E9%A1%B9%2C%E6%B1%82P%E7%82%B9%E5%9D%90%E6%A0%87.)
椭圆x²/9+y²/4=1上点P到其右焦点的距离是长轴两端点到右焦点的距离的等差中项,求P点坐标.
椭圆x²/9+y²/4=1上点P到其右焦点的距离是长轴两端点到右焦点的距离的等差中项,求P点坐标.
椭圆x²/9+y²/4=1上点P到其右焦点的距离是长轴两端点到右焦点的距离的等差中项,求P点坐标.
由方程得到a=3,b=2,c=√5 ,右焦点F(√5 ,0)
则长轴两端点到右焦点的距离:a+c=3+√5和a-c=3-√5
等差中项d=3
设P(x,y),解下面的方程组即可
d=√(x-√5)²+y²=3
x²/9+y²/4=1
解得x1=0, x2=18/√5(舍去)
有两个满足条件的P(0,2),(0,-2)