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  4. The sum of the distances of any point on the ellipse 3x2+4y2=24 from its foci, is:

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Q. The sum of the distances of any point on the ellipse $ 3{{x}^{2}}+4{{y}^{2}}=24 $ from its foci, is:

KEAMKEAM 2001

Solution:

Equation of ellipse is $ 3{{x}^{2}}+4{{y}^{2}}=24 $ $ \Rightarrow $ $ \frac{{{x}^{2}}}{8}+\frac{{{y}^{2}}}{6}=1 $ Here $ a=2\sqrt{2} $ and $ b=\sqrt{6} $ . The sum of the distances of any point on the ellipse from its foci is $ 2a=4\sqrt{2} $ .