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# A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

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The path described here is an ellipse represented as follows:
Comparing to a standard form or an ellipse, we get $2a = 10 \rightarrow a = 5$ and $2c = 8 \rightarrow c = 4$
We know that $c^2 = a^2 - b^2 \rightarrow b = \sqrt{25-16} = \sqrt 9 = 3$
Therefore, the equation of the path traced $= \large\frac{x^2}{25}$$+\large\frac{y^2}{9}$$ = 1$
answered Apr 8, 2014