The normal at P of the parabola y²=4ax whose focus is S meets it again at Q.If PQ subtends a right angle at its vertex, show that

SP=SQ/3=3a

let P be (x1,y1), equation of normal at P is: y-y1=(-y'/2a)(x-x')..equa.(1),in (1) express x in terms of y, y^2=4ax...equa.(2),

solve the system of two equations (1) and (2). this will yield the coordinates of Q. vertex is (0.0).O is origin, let PO be inclined at alpha to x-axis and QO be inclened at beta. impose the condition l(alphs)-(beta)l=pi/2, this condition will give you the answer that is required.

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