JEE Advance - Mathematics (1994 - No. 45)
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 $$PQ$$.
The line PQ always passes through the point (4, 0), and the locus of the midpoint of PQ is y^2 = 2(x - 4).
The line PQ always passes through the point (2, 0), and the locus of the midpoint of PQ is y^2 = x - 2.
The line PQ always passes through the point (0, 4), and the locus of the midpoint of PQ is x^2 = 2(y - 4).
The line PQ always passes through the point (0, 2), and the locus of the midpoint of PQ is x^2 = y - 2.
The line PQ always passes through the point (4, 4), and the locus of the midpoint of PQ is (x-2)^2 + (y-2)^2 = 4.
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