已知抛物线的顶点在原点,焦点在x轴上截直线2x-y-4=0所得弦长为3根号5
问题描述：
已知抛物线的顶点在原点,焦点在x轴上截直线2x-y-4=0所得弦长为3根号5
答
y^2=2px
y=2(x-2)
4(x-2)^2=2px
x^2-(4+p/2)x+4=0
x1+x2=4+p/2
x1x2=4
(y1-y2)^2=4(x1-x2)^2
(x1-x2)^2+(y1-y2)^2=(3根号5)^2
5(x1-x2)^2=45
(4+p/2)^2-4*4=9
p=-18,或2
y^2=-36x,或y^2=4x