已知椭圆x^2/a^2+y^2/b^2=1(a>b>0)的右焦点F在抛物线y^2=-4x的准线上,(1)若椭圆的离心率e=1/3,求椭圆的方程;(2)设过点F的直线l交椭圆于C,D,两点,若直线l绕点F任意转动时恒有 {OC}^2+{OD}^2
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![已知椭圆x^2/a^2+y^2/b^2=1(a>b>0)的右焦点F在抛物线y^2=-4x的准线上,(1)若椭圆的离心率e=1/3,求椭圆的方程;(2)设过点F的直线l交椭圆于C,D,两点,若直线l绕点F任意转动时恒有 {OC}^2+{OD}^2](/uploads/image/z/7015600-64-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%3Eb%3E0%29%E7%9A%84%E5%8F%B3%E7%84%A6%E7%82%B9F%E5%9C%A8%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D-4x%E7%9A%84%E5%87%86%E7%BA%BF%E4%B8%8A%2C%281%29%E8%8B%A5%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87e%3D1%2F3%2C%E6%B1%82%E6%A4%AD%E5%9C%86%E7%9A%84%E6%96%B9%E7%A8%8B%3B%282%29%E8%AE%BE%E8%BF%87%E7%82%B9F%E7%9A%84%E7%9B%B4%E7%BA%BFl%E4%BA%A4%E6%A4%AD%E5%9C%86%E4%BA%8EC%2CD%2C%E4%B8%A4%E7%82%B9%2C%E8%8B%A5%E7%9B%B4%E7%BA%BFl%E7%BB%95%E7%82%B9F%E4%BB%BB%E6%84%8F%E8%BD%AC%E5%8A%A8%E6%97%B6%E6%81%92%E6%9C%89+%7BOC%7D%5E2%2B%7BOD%7D%5E2)
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