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If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is

(a) x = 1 

(b) 2x + 1 = 0

(c) x = –1 

(d) 2x – 1 = 0

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2 Answers

(c) : From a property of the parabola, the perpendicular tangents intersect at the directrix. The equation of directrix is x = –1, hence this is the locus of point P.

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(2) x = –1 

The locus of perpendicular tangents is directrix. i.e, x = –a; x = –1

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