Question

A man running round a racecourse 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 is

• A. $18\pi$ square metres
• B. $15\pi$ square metres
• C. $12\pi$ square metres
• D. $8\pi$ square metres

Answer 1

The correct option is B $15\pi$ square metres

$P{F}_1+P{F}_2=10$
$\Rightarrow 2a=10\Rightarrow a=5$
$F_1{F}_2=8\Rightarrow 2c=8\Rightarrow c=4$
$a^2=b^2+c^2\Rightarrow b^2=3^2\Rightarrow b=3$

$Area=\pi ab=\pi \times 3\times 5=15\pi$

Therefore, the answer is $15\pi m^2$