Question

If tangent to the curve 16y² + 9x² = 144, intersects the axes at A and B, then the minimum length of the segment AB.

(1) 5
(2) 8
(3) 7
(4) 4

Answer 1

Correct option is (3) 7

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

Equation of tangent \(\frac x4 \cos \theta + \frac y3 \sin\theta =1\)

\(A (4\sec\theta, 0)B(0, 3cosec\theta)\)

\(AB = \sqrt{16\sec^2 + acosec^2\theta}\)

\(= \sqrt{25 + (4 \tan\theta - 3\cot\theta)^2 + 24} \ge \sqrt{49} \ge 7\)

\(AB_{min} = 7\)