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 metres. The area of the path he encloses in square metres is-

• A. 15p
• B. 12p
• C. 18p
• D. 8p

Answer 1

Answer: (A)

15p

Answer 2

Clearly the race course is an ellipse with flag-posts as its foci. If a and b are the semi-major and minor axes of the ellipse, then

2a = 10 and 2 ae = 8 Ž a = 5, e = $\frac{4}{5}$

Now, b² = a² (1 – e²) Ž b² = 25$\left( 1 - \frac{16}{25} \right)$ = 9

Ž b = 3.

\ the area of the ellipse = p ab = 15p.