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

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 point of concurrency of chord of contact A B of the circle x2+y2=12 is (A) (x2/9)+(y2/16)=1 (B) (x2/12)+(y2/4)=1 (C) (x2/12)+(y2/16)=1 (D) (x2/6)+(y2/8)=1

Tardigrade Admin · Accepted Answer

Correct answer is (a) (x2/9)+(y2/16)=1

$\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1$

$\frac{x ^{2}}{12} + \frac{y ^{2}}{4} = 1$

$\frac{x ^{2}}{12} + \frac{y ^{2}}{16} = 1$

$\frac{x ^{2}}{6} + \frac{y ^{2}}{8} = 1$

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

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 point of concurrency of chord of contact AB of the circle x2+y2=12 is

9x2​+16y2​=1

12x2​+4y2​=1

12x2​+16y2​=1

6x2​+8y2​=1

Correct answer is (a) 9x2​+16y2​=1

$\frac{x ^{2}}{9} + \frac{y ^{2}}{16} = 1$

$\frac{x ^{2}}{12} + \frac{y ^{2}}{4} = 1$

$\frac{x ^{2}}{12} + \frac{y ^{2}}{16} = 1$

$\frac{x ^{2}}{6} + \frac{y ^{2}}{8} = 1$

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