Through The Vertex O of Parabola y2 = 4x, Chords OP and OQ are Drawn At Right Angles To One Another. The Locus Of The Middle Point Of PQ is

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Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another. The locus of the middle point of PQ is


Correct option is

y2 = 2x – 8

y2 = 4x = 4ax say   …. (1)

 a = 1,  let   P = (t12, 2t1) : Q(t22, 2t2),

slope of OP = 

Since .

Let  be the middle point of chord PQ. Then



 is y2 = 2x – 8.



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