若A为抛物线Y=1/4X^2的顶点,过抛物线焦点的直线交抛物线于B,C两点,则向量AB*AC=?
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若A为抛物线Y=1/4X^2的顶点,过抛物线焦点的直线交抛物线于B,C两点,则向量AB*AC=?
若A为抛物线Y=1/4X^2的顶点,过抛物线焦点的直线交抛物线于B,C两点,则向量AB*AC=?
若A为抛物线Y=1/4X^2的顶点,过抛物线焦点的直线交抛物线于B,C两点,则向量AB*AC=?
抛物线方程化为:
x²=4y
则焦点坐标为(0,1),A点坐标为(0,0)
设B(x1,y1),C(x2,y2)
设直方程为y=kx+1
联立{y=kx+1
{x²=4y
得x²-4kx-4=0
∴x1+x2=4k,x1*x2=-4
∴y1*y2=1/4x1²*1/4x2²=1/16*(x1*x2)²=1
∴AB*AC=(x1,y1)*(x2,y2)=x1x2+y1y2=-4+1=-3