Question

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

Answer 1

$PS + PS S ^{\prime}=10$
$2 a =10$
$a =5$
$2 ae =8$
$ae =4$
$e =4 / 5$
$b ^{2}= a ^{2}\left(1- e ^{2}\right)$
$b ^{2}=25$$\left(1-\frac{16}{25}\right)$
$b =3$
$A =\pi ab =\pi \times 5 \times 3$
$=15 \pi $