If the normal at P to the parabola y2=4ax meetsthe parabola again at Q such that PQ subtends aright angle at the vertex of the parabola, then thecoordinates of P are

Let the coordinates of P be am2,−2am  and Q be am2,−2am′ then −2amam2×−2am′am′2=−1⇒mm′=−4Normal at P,y=mx−2am−am3 Since it passesthrough Q−2a−4m⊨am16m2−2am−am3=0⇒m4+2m2−8=0⇒m=±2 and thecoordinates of P are (2a,±22a).