Conic Sections Question 477
Question: A man running round a race-course notes that the sum of the distance 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
[MNR 1991; UPSEAT 2000]
Options:
A) $ 15\pi $
B) $ 12\pi $
C) $ 18\pi $
D) $ 8\pi $
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ 2a=10m $ and $ 2ae=8m $ ; $ e=\frac{4}{5},a=5m $
$ b^{2}=a^{2}(1-e^{2})=9 $
therefore $ b=3 $
Thus, required area $ =\pi ab=15\pi sq.metre $ .
BETA
