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  4. The radius of the circle passing through the foci of the ellipse (x2/16)+(y2/9)=1 and having its centre (0,3), is

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Q. The radius of the circle passing through the foci of the ellipse $ \frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1 $ and having its centre $ (0,3), $ is

Bihar CECEBihar CECE 2015

Solution:

Let e be the eccentricity of the ellipse $ \frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{9}=1 $ Then, $ e=\sqrt{1-\frac{9}{16}}=\frac{\sqrt{7}}{4} $ So, coordinates of the foci of the ellipse are $ (\pm \sqrt{7,0}) $ . The radius of the circle having centre at (0,3) and passing through foci $ =\sqrt{{{(0-\sqrt{7})}^{2}}+{{(3-0)}^{2}}}=4 $