AOB is the positive quadrant of the ellipse f | vedclass

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(D) The equation of the ellipse is $\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1$. Here,$a=5$ and $b=3$. The area of the positive quadrant $OAB$ is $\frac{1}

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$\frac{15}{4}(\pi-2)$

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(D) The equation of the ellipse is $\frac{x^2}{5^2} + \frac{y^2}{3^2} = 1$. Here,$a=5$ and $b=3$. The area of the positive quadrant $OAB$ is $\frac{1}{4} 	imes \pi ab = \frac{1}{4} 	imes \pi 	imes 5 	imes 3 = \frac{15\pi}{4}$. The area of the triangle $OAB$ with vertices $(0,0), (5,0), (0,3)$ is $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 5 	imes 3 = \frac{15}{2}$. The area between the arc $AB$ and the chord $AB$ is the area of the quadrant minus the area of the triangle. Area $= \frac{15\pi}{4} - \frac{15}{2} = \frac{15}{4}(\pi - 2)$ sq. units.

$AOB$ is the positive quadrant of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ in which $OA=5, OB=3$. The area between the arc $AB$ and the chord $AB$ of the ellipse in sq. units is

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