Through the vertex 'O' of parabola y^2=...

Through the vertex 'O' of parabola `y^2=4x`, chords OP and OQ are drawn at right angles to one another. Show that for all positions of P, PQ cuts the axis of the parabola at a fixed point. Also find the locus of the middle point of PQ.

A

1) `y ^(2) =x+8`

B

2) `y ^(2) =-2 +8`

C

3) `y ^(2) =2x -8`

D

4) `y ^(2) =x-8`

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The correct Answer is:

C

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