设C坐标是(x,y)
那么有|x+1|=根号[(x-1)^2+y^2]
即有x^2+2x+1=x^2-2x+1+y^2
即有方程是y^2=4x
(2)设直线L方程是y=kx+1,P(x1,y1),Q(x2,y2)
代入到抛物线中有k^2x^2+2kx+1=4x,即有k^2x^2+(2k-4)x+1=0
以PQ为直径的圆过原点,则有x1x2+y1y2=0
x1x2+(kx1+1)(kx2+1)=0
(1+k^2)x1x2+k(x1+x2)+1=0
(1+k^2)*1/k^2+k*(4-2k)/k^2+1=0
1+k^2+4k-2k^2+k^2=0
4k+1=0
k=-1/4
即直线方程是y=-x/4+1