Correct option is (3) 7
\(\frac{x^2}{16} + \frac{y^2}9 = 1\)
Equation of tangent \(\frac x4 \cos \theta + \frac y3 \sin\theta =1\)
\(A (4\sec\theta, 0)B(0, 3cosec\theta)\)
\(AB = \sqrt{16\sec^2 + acosec^2\theta}\)
\(= \sqrt{25 + (4 \tan\theta - 3\cot\theta)^2 + 24} \ge \sqrt{49} \ge 7\)
\(AB_{min} = 7\)