The locus of the point, whose chord of contact w.r.t the circle $x^{2} + y^{2} = a^{2}$ makes an angle $2 α$ at the centre of the circle is

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Solution

The correct option is C

Let $P (x_{1}, y_{1})$ be a point on the locus
Let PA and PB be the tangent drawn from P to the circle $x^{2} + y^{2} = a^{2}$
And the chord AB makes an angle $2 α$ at the origin O(0, 0) the centre of the circle.
Then $∠ A O P = α, c o s α = \frac{O A}{O P} \Rightarrow s e c α = \frac{O P}{O A}$
$\Rightarrow O P^{2} = O A^{2} s e c^{2} α \Rightarrow x_{1}^{2} + y_{1}^{2} = a^{2} s e c^{2} α ∴ L o c u s o f (x_{1}, y_{1}) i s x^{2} + y^{2} = a^{2} s e c^{2} α$

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The locus of the point, whose chord of contact w.r.t the circle x2+y2=a2 makes an angle 2α at the centre of the circle is

The locus of the point, whose chord of contact w.r.t the circle $x^{2} + y^{2} = a^{2}$ makes an angle $2 α$ at the centre of the circle is