Question

A man running round a race course notes that the sum of the distances of two flag posts from him is 8 metres. The area of the path he encloses in square meters if the distance between flag is 4 is

• A. 15π
• B. 12π
• C. 18π
• D. 8$\sqrt{3}$π

Answer 1

Answer: (D)

8$\sqrt{3}$π

Answer 2

By the given condition, the man running along the shape of an ellipse with the two flag posts as foci.

∴ Given 2ae = 4, a also SP+S’P = 8 = 2a ⇒ a = 4

∴ ae = 2.

∴ a²e² = 4

∴ a² – b² = 4

b² = 12

The area enclosed = πab = 8$\sqrt{3}$π.