已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a+u=
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![已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a+u=](/uploads/image/z/2640385-1-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFy%26%23178%3B%3D2px%28p%3E0%29.%E8%BF%87%E7%82%B9E%28m%2C0%29.%28m%E4%B8%8D%E7%AD%89%E4%BA%8E0%29%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%BA%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%BA%8E%E7%82%B9M%2CN%2C%E4%BA%A4y%E8%BD%B4%E4%BA%8E%E7%82%B9P%2C%E5%90%91%E9%87%8FPM%E7%AD%89%E4%BA%8Ea%E5%90%91%E9%87%8FME%2C%E5%90%91%E9%87%8FPN%3Du%E5%90%91%E9%87%8FNE%2C%E5%88%99a%EF%BC%8Bu%3D)
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已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a+u=
已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a+u=
已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a+u=
分别设M,N,P的坐标为(x1,y1),(x2,y2),(x0,y0),
∵PM=λME,PN=μNE,
∴(x1-x0,y1-y0) =λ(m-x1,-y1) (x2-x0,y2-y0)=μ(m-x2,-y2) ,可得到x1,x2,y1,y2,
直线MN的方程为:y-y1x-x1=y2-y1x2-x1,可用y来表示x,
然后带到抛物线表达式中,
根据韦达定理,求出y1,y2的积、和,分别等于之前算出的y1,y2的积、和.从而得出λ+μ=-1.