Sum of focal distances of any point on conic frac{{{x^2}}}{{25}} + frac{{{y^2}}}{{16}} = 1 is

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10-2. Parabola, Ellipse, Hyperbola

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The sum of the focal distances of any point on the conic $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$ is

A

$10$

B

$9$

C

$41$

D

$18$

Solution

(a) For any point $P$ on the ellipse have focus $S$ and $S' $ $SP + S'P = 2a$

For $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1$

Sum of focal distances = $2 \times 5 = 10.$

Standard 11

Mathematics

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