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

Question

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 (A) 3 x+4 y=12 √3 (B) 3 x+4 y=6 √2 (C) 4 x+3 y=12 √3 (D) 4 x+3 y=6 √2

Tardigrade Admin · Accepted Answer

Correct answer is (b) 3 x+4 y=6 √2

$3 x + 4 y = 123$

$3 x + 4 y = 62$

$4 x + 3 y = 123$

$4 x + 3 y = 62$

Correct answer is (b) $3 x + 4 y = 62$

Q. A tangent is drawn at any point P(4cosθ,3sinθ) on the ellipse 9x2+16y2=144 and on it is taken a point Q(α,β) from which pair of tangents QA and QB are drawn to the circle x2+y2−12=0. The locus of the circumcentre of triangle QAB if θ=4π​ is

3x+4y=123​

3x+4y=62​

4x+3y=123​

4x+3y=62​

Correct answer is (b) 3x+4y=62​

$3 x + 4 y = 123$

$3 x + 4 y = 62$

$4 x + 3 y = 123$

$4 x + 3 y = 62$

Correct answer is (b) $3 x + 4 y = 62$