Question

The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^2}{16}+\frac{y^2}{81}=1$ and the coordinate axes is

• A. 26
• B. 12
• C. 18
• D. 36

Answer 1

Answer: (D)

$\Delta =\frac{1}{2}\left(\frac{a}{\cos \theta }\right)\left(\frac{b}{\sin \theta }\right)=\frac{ab}{\sin 2\theta }\ge ab$
$\therefore {\Delta }_{\min .}=(4)(9)=36$