Question

直线y=x+1截抛物线y²=2px所得弦长为2,此抛物线方程为（    ）

A.y²=2x                                     B.y²=6x

C.y²=-2x或y²=6x                       D.以上都不对

Answer 1

解析：将y=x+1代入y²=2px，得x²+(2-2p)x+1=0,x₁+x₂=2p-2,x₁x₂=1,d=|x₁-x₂|=2,p=-1或p=3.

故选C.

答案:C