已知过抛物线C:y^2=2px(p>0)的焦点F的直线l交抛物线于A、B两点其坐标分别为A(x1,y1),B(x2,y2),而且都满足x1x2=1(1)求抛物线C的方程;(2)过原点O作向量OK,使向量OK⊥向量AB,垂足为K,求点K的轨迹
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![已知过抛物线C:y^2=2px(p>0)的焦点F的直线l交抛物线于A、B两点其坐标分别为A(x1,y1),B(x2,y2),而且都满足x1x2=1(1)求抛物线C的方程;(2)过原点O作向量OK,使向量OK⊥向量AB,垂足为K,求点K的轨迹](/uploads/image/z/7207368-24-8.jpg?t=%E5%B7%B2%E7%9F%A5%E8%BF%87%E6%8A%9B%E7%89%A9%E7%BA%BFC%EF%BC%9Ay%5E2%3D2px%28p%3E0%29%E7%9A%84%E7%84%A6%E7%82%B9F%E7%9A%84%E7%9B%B4%E7%BA%BFl%E4%BA%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%BA%8EA%E3%80%81B%E4%B8%A4%E7%82%B9%E5%85%B6%E5%9D%90%E6%A0%87%E5%88%86%E5%88%AB%E4%B8%BAA%28x1%2Cy1%29%2CB%28x2%2Cy2%29%2C%E8%80%8C%E4%B8%94%E9%83%BD%E6%BB%A1%E8%B6%B3x1x2%3D1%EF%BC%881%EF%BC%89%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BFC%E7%9A%84%E6%96%B9%E7%A8%8B%EF%BC%9B%EF%BC%882%EF%BC%89%E8%BF%87%E5%8E%9F%E7%82%B9O%E4%BD%9C%E5%90%91%E9%87%8FOK%2C%E4%BD%BF%E5%90%91%E9%87%8FOK%E2%8A%A5%E5%90%91%E9%87%8FAB%2C%E5%9E%82%E8%B6%B3%E4%B8%BAK%2C%E6%B1%82%E7%82%B9K%E7%9A%84%E8%BD%A8%E8%BF%B9)
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