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Through the vertex O of a parabola y^(2)...

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

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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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