抛物线顶点在原点 焦点在X轴这个抛物线截直线2X-Y-4=0得弦长3倍根号5 求抛物线~

设抛物线解析式是y^2=2px.
y=2x-4代入得:4x^2+16-16x=2px
2x^2-(8+p)x+8=0
x1+x2=(8+p)/2
x1x2=4
(x1-x2)^2=(x1+x2)^2-4x1x2=(8+p)^2/4-16=(64+16p+p^2-64)/4=(16p+p^2)/4
弦长=根号(1+K^2)*|X1-X2|
3根号5=根号(1+4)*根号[(16p+p^2)/4]
9=(16p+p^2)/4
p^2+16p-36=0
(p+18)(p-2)=0
p=-18,
p=2
所以,方程是:y^2=-36x或者y^2=4x.