Question

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

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

Answer 1

The correct option is A $15\pi$

the path described here is an ellipse

now comparing the question with a standard ellipse

we will get $2a=10$ and $2c=8$

and we know $c^2=a^2-b^2$

on putting value of $a$ and $c$ in above equation

$b=3$

hence we know $A=\pi \left(a\right)\left(b\right)$

hence $A=\pi \times \left(5\right)\times \left(3\right)$

hence $A=15\pi$