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

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

KCETKCET 2000Conic Sections

Solution:

Ellipse is $\frac{x^{2}}{8} +\frac{y^{2}}{6} = 1 $.
Here $a^{2}= 8 $
$ \Rightarrow a=2\sqrt{2}$
sum of focal distances $ = 2a=4\sqrt{2}$