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.

Question

$\begin {array} {1 1} (A)\;\large\frac{x^2}{25}-\large\frac{y^2}{9}=1 & \quad (B)\;\large\frac{x^2}{9}+\large\frac{y^2}{25}=1 \\ (C)\;\large\frac{y^2}{25}-\large\frac{x^2}{9}=1 & \quad (D)\;\large\frac{x^2}{25}+\large\frac{y^2}{9}=1 \end {array}$