Let A,B and C are three points on ellipse frac{x^2}{25}+frac{y^2}{16}=1 where line joing A ,,&,,

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10-2. Parabola, Ellipse, Hyperbola

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Let $A,B$ and $C$ are three points on ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$where line joing $A \,\,\&\,\, C$ is parallel to the $x-$axis and $B$ is end point of minor axis whose ordinate is positive then maximum area of $\Delta ABC,$ is-

A

$12\sqrt 3$

B

$20$

C

$15\sqrt 3$

D

$20\sqrt 3$

Solution

Area $=\frac{1}{2} 10 \cos \theta(4+4 \sin \theta)$

$\frac{\mathrm{d} \mathrm{A}}{\mathrm{d} \theta}=0 \Rightarrow \theta=\frac{\pi}{6}$

$A_{\max }=15 \sqrt{3}$

Standard 11

Mathematics

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