P is a variable point on the ellipse frac{x^2 | vedclass

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(A) Let the ellipse be $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. The major axis $AA'$ lies along the $x$-axis with coordinates $A = (a, 0)$ and $A' = (

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$|ab|$

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(A) Let the ellipse be $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. The major axis $AA'$ lies along the $x$-axis with coordinates $A = (a, 0)$ and $A' = (-a, 0)$.Let point $P$ be $(a \cos 	heta, b \sin 	heta)$.The area of $\Delta APA'$ is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Base $AA' = 2a$ and height is the absolute value of the $y$-coordinate of $P$,which is $|b \sin 	heta|$.Area $= \frac{1}{2} 	imes (2a) 	imes |b \sin 	heta| = |ab \sin 	heta|$.Since the maximum value of $|\sin 	heta|$ is $1$,the maximum area is $|ab|$.

$P$ is a variable point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $AA'$ as the major axis. Then the maximum value of the area of $\Delta APA'$ is

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