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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
15π
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B
12π
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C
18π
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D
8π
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Solution

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 $$A=\pi(a)(b)$$ 
hence $$A=\pi\times(5)\times(3)$$
hence $$A=15\pi$$

Mathematics

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