are on the parabola .

If the chord PQ passes through the focus of the parabola and the normals at P and Q meet at R, show that the locus of R is given by .

Since the chord is a focal chord, pq=-1. and q=-1/p

then .

the equations of the normals are

_1 and _2

1 and

2

solving these two

and

now my problem is I have the parametric equation for the locus of R but i don't know how to get the cartesian equation from here.

Thanks