Let the point of intersection of the required tangent be (h,k) . Then the equation of tangent through the point to the parabola y2=8xis, (y2−8x)(k2−8h)=[yk−4(x+h)]2 Now, the equation of tangent to the vertex of parabola is x=0. So, y2(k2−8h)=(yk−4h)2 y2k2−8hy2=y2k2+16h2−8hky y2−ky+2h=0 Therefore, the roots are y1 and y2. |y1−y2|=
√k2−8h
1
4=√k2−8h k2−8h=16 k2=8(h+2) Take the locus of point (h,k) y2=8(x+2)