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

(a) Here $2a = 10\ m$ and $2ae = 8m$;

$e = \frac{4}{5},\,a = 5m$

${b^2} = {a^2}(1 – {e^2}) = 9$

==> $b = 3$

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

Standard 11

Mathematics

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