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The area between the ellipse $\large\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}$=$1$ and its auxillary circle is

\[\begin{array}{1 1}(1)\pi b(a-b)&(2)2\pi a(a-b)\\(3)\pi a(a-b)&(4)2\pi b(a-b)\end{array}\]

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The area of the ellipse $ \large\frac{x^2}{a^2} +\frac{y^2}{b^2} $$=1$ is $\pi a b$
The equation of the auxiliary circle of the ellipse $ \large\frac{x^2}{a^2} +\frac{y^2}{b^2} $ is $x^2+y^2$
Area of the auxiliary circle is
$x^2 +y^2 =a^2 \pi a^2$
Area between the auxiliary circle ad the ellipse $ = \pi a^2 - \pi ab$
$\qquad= \pi a (a-b)$
Hence 3 is the correct answer.
answered May 21, 2014 by meena.p

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