question_answer

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 in square metres is

A) \[15\pi \]           

B)        \[12\pi \]   

C) \[18\pi \]           

D)        \[8\pi \]

Correct Answer: A

Solution :

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