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  4. The minimum area of a triangle formed by any tangent to the ellipse (x2/16)+(y2/81)=1 and the coordinate axes is

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Q. 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

Conic Sections

Solution:

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