P is a point on the locus of the mid-points of thechords of the parabola y2=4ax passing throughthe vertex of the parabola; S is the focus of theparabola and the line joining S and P is producedto meet the parabola at Q. If the ordinate of P isequal to its abscissa, coordinates of Q are

O(0, 0) is the vertex and Rat2,2at is any pointon the parabola. at2/2,2at/2 is the mid-point ofthe chord OR. Whose locus is y2=2ax coordinatesof P on this locus are (2a, 2a), focus is S(a, 0). Equation of SP is y=2(x−a) which meetsy2=4ax at the point Q for which  4(x−a)2=4ax⇒x2−3ax+a2=0 which is not satisfied by thepoints in (a), (b) or (c).