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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.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
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  13. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

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  14. Two parabola have the same focus. If their directrices are the x-axis ...

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  17. The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the l...

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