This question is an exact duplicate of:
Let normals are drawn to the parabola $y^2=8x$ from any point on the line $y=−4$ . Find the locus of vertices of triangle formed by the corresponding tangents ?
Tried based on this: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.630.3708&rep=rep1&type=pdf
There are several conditions on the point A(t,−4) on the line $y=−4$ .
As locus is a part of the hyperbola $y=8x$ , but i find it very difficult to find.