1. Tardigrade
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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 circumcentre of triangle QAB if θ=(π/4) 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 circumcentre of triangle $QAB$ if $\theta=\frac{\pi}{4}$ is

Conic Sections

Solution:

Correct answer is (b) $3 x+4 y=6 \sqrt{2}$