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  4. A tangent is drawn at any point P(4 cos θ, 3 sin θ) on the ellipse 9 x2+16 y2=144 and on it is taken a point Q(α, β) from which pair of tangents Q A and Q B are drawn to the circle x2+y2-12=0. The locus of the point of concurrency of chord of contact A B of the circle x2+y2=12 is

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Q. A tangent is drawn at any point $P(4 \cos \theta, 3 \sin \theta)$ on the ellipse $9 x^2+16 y^2=144$ and on it is taken a point $Q(\alpha, \beta)$ from which pair of tangents $Q A$ and $Q B$ are drawn to the circle $x^2+y^2-12=0$.
The locus of the point of concurrency of chord of contact $A B$ of the circle $x^2+y^2=12$ is

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Solution:

Correct answer is (a) $\frac{x^2}{9}+\frac{y^2}{16}=1$