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At any point P on the parabola y^2 - 2y - 4x + 5 = 0 a tangent is drawn which meets the directrix at Q.

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At any point P on the parabola y2 - 2y - 4x + 5 = 0 a tangent is drawn which meets the directrix at Q. Find the locus of point R, which divides QP externally in the ratio 1/2 : 1.

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Best answer

Given equation can be rewritten as

(y - 1)2 = 4(x - 1)

whose parametric coordinates are

x - 7 = t2 and y - 1 = 2t

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