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
B
12π
C
18π
D
8π

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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