Q. A man running round a race course notes that the sum of the distances of two flag posts from him is always 10m and the distance between the flag posts is 8m. The area of the path he encloses (in square metre) is
A) $15\pi$
B) $12\pi$
C) $18\pi$
D) $8\pi$
Explanation
(a)
Let $P$ is the position of man and $S,\ S'$ are position of flags, then
$SP + S^{'}P = 10 = 2a \Rightarrow a = 5$
$\therefore SS^{'} = 2ae = 8 \Rightarrow e = \frac{4}{5}$
Now, $e^{2} = 1 - \frac{b^{2}}{a^{2}} \Rightarrow \frac{16}{25} = 1 - \frac{b^{2}}{25}$
$\Rightarrow b^{2} = 9 \Rightarrow b = 3$
Area of ellipse$= \pi ab = 15\pi\ sq\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.