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  • The minimum area of the triangle formed by any tangent to the ellipse<img alt="\mathrm{ \frac{x^2}{16}+\frac{y^2}{81}=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20%5Cfrac

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

Option: 1

36


Option: 2

30


Option: 3

32


Option: 4

34


Answers (1)

best_answer

\mathrm{\text { An equation of tangent to the ellipse } \frac{x^2}{16}+\frac{y^2}{81}=1}

\mathrm{\frac{x}{4} \cos \theta+\frac{y}{9} \sin \theta=1}

\mathrm{\text { Coordinates of } A \text { and } B \text { are }(4 \sec \theta, 0) \text { and }(0,9 \operatorname{cosec} \theta)} respectively

\mathrm{\text { Area of } \triangle O A B=\frac{1}{2} \frac{36}{|\sin \theta \cos \theta|}=\frac{36}{\sin 2 \theta}}

So, minimum value of area is 36.

Posted by

Sanket Gandhi

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