A man running round a race-course notes that sum of distance of two flag-posts from him is always 10

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10-2. Parabola, Ellipse, Hyperbola

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A man running round a race-course notes that the sum of the distance of two flag-posts from him is always $10\ metres$ and the distance between the flag-posts is $8\ metres$. The area of the path he encloses in square metres is

A

$15\ \pi$

B

$12\ \pi$

C

$18\ \pi$

D

$8\ \pi$

Solution

Here $2 \mathrm{a}=10 \mathrm{m}$ and $2 \mathrm{ae}=8 \mathrm{m} ; \mathrm{e}=\frac{4}{5}, \mathrm{a}=5 \mathrm{m}$

$\therefore \mathrm{b}^{2}=\mathrm{a}^{2}\left(1-\mathrm{e}^{2}\right)=9 \quad \Rightarrow \quad \mathrm{b}=3$

Thus, required area $=\pi \mathrm{ab}=15 \pi$ sq. metre.

Standard 11

Mathematics

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(JEE MAIN-2019)