已知抛物线的顶点在原点焦点在Y轴正半轴上,点P(m,4)已知抛物线G的顶点在原点,焦点在y轴正半轴上,点p(m,4)到其焦准线的距离为5,若过G的焦点的直线依次与抛物线G及圆x^2+(y-1)^2=1交于A\C\D\
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![已知抛物线的顶点在原点焦点在Y轴正半轴上,点P(m,4)已知抛物线G的顶点在原点,焦点在y轴正半轴上,点p(m,4)到其焦准线的距离为5,若过G的焦点的直线依次与抛物线G及圆x^2+(y-1)^2=1交于A\C\D\](/uploads/image/z/3023798-14-8.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9C%A8%E5%8E%9F%E7%82%B9%E7%84%A6%E7%82%B9%E5%9C%A8Y%E8%BD%B4%E6%AD%A3%E5%8D%8A%E8%BD%B4%E4%B8%8A%2C%E7%82%B9P%EF%BC%88m%2C4%EF%BC%89%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFG%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9C%A8%E5%8E%9F%E7%82%B9%2C%E7%84%A6%E7%82%B9%E5%9C%A8y%E8%BD%B4%E6%AD%A3%E5%8D%8A%E8%BD%B4%E4%B8%8A%2C%E7%82%B9p%EF%BC%88m%2C4%EF%BC%89%E5%88%B0%E5%85%B6%E7%84%A6%E5%87%86%E7%BA%BF%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA5%2C%E8%8B%A5%E8%BF%87G%E7%9A%84%E7%84%A6%E7%82%B9%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%BE%9D%E6%AC%A1%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFG%E5%8F%8A%E5%9C%86x%5E2%2B%28y-1%29%5E2%3D1%E4%BA%A4%E4%BA%8EA%5CC%5CD%5C)
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已知抛物线的顶点在原点焦点在Y轴正半轴上,点P(m,4)已知抛物线G的顶点在原点,焦点在y轴正半轴上,点p(m,4)到其焦准线的距离为5,若过G的焦点的直线依次与抛物线G及圆x^2+(y-1)^2=1交于A\C\D\
已知抛物线的顶点在原点焦点在Y轴正半轴上,点P(m,4)
已知抛物线G的顶点在原点,焦点在y轴正半轴上,点p(m,4)到其焦准线的距离为5,若过G的焦点的直线依次与抛物线G及圆x^2+(y-1)^2=1交于A\C\D\B四点,试证明|AC|*|BD|为定值,
已知抛物线的顶点在原点焦点在Y轴正半轴上,点P(m,4)已知抛物线G的顶点在原点,焦点在y轴正半轴上,点p(m,4)到其焦准线的距离为5,若过G的焦点的直线依次与抛物线G及圆x^2+(y-1)^2=1交于A\C\D\
抛物线为x^2=4y
焦点与圆心重合,直线斜率不存在时与抛物线只有一个交点,舍
k存在,设直线y-1=kx
设A(x1,y1),B(x2,y2)
利用抛物线定义,到焦点距离=到准线距离,所以AG=y1+1,圆半径为1,所以AC=y1
同理BD=y2,所以|AC|*|BD|=y1*y2
直线抛物线联立方程,消去X,得要关于y的一元二次方程,y1y2=c/a=1
得证