# Q7.    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.

As we know that if a point moves in a plane in such a way that its distance from two-point remain constant then the path is an ellipse.

Now, According to the question,

the distance between the point from where the sum of  the distance from a point is constant =  10

Now, the distance between the foci=8

Now, As we know the relation,

Hence the equation of the ellipse is,

Hence the path of the man will be

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