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Chords of the parabola $y^{2} = 4 x$ touch the hyperbola $x^{2} - y^{2} = 1$ . The locus of the point of intersection of the tangents drawn to the parabola at the extremities of such chords is

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a circle

a parabola

an ellipse

a rectangular hyperbola

answer is C.

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Detailed Solution

The chord of contact $y y_{o} = 2 (x + x_{o})$ of the point $P (x_{o}, y_{o})$ w.r.t the parabola is tangent to the hyperbola $x^{2} - y^{2} = 1 i f f 2 x_{0}^{2} + y_{0}^{2} = 4$ . Locus of P is the ellipse $2 x^{2} + y^{2} = 4$

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