A set of parallel chords of the parabola y2=4ax have their midpoints on

Let points Pat12,2at1 and Qat22,2at2 lie on the  parabola y2=4ax Here, points P and Q are variable. But the slope of chord PQ , mPQ=2t1+t2 is constant.  Now, let the midpoint of PQ be R(h,k) . Then, k=2at1+2at22 or k=at1+t2=2m∴ y=2m which is a line parallel to the axis of the parabola.