A man running a race course notes that the sum of his distances from the two flag posts is always 10m and the distance between the flag posts is 8m.

Q: A man running a race course notes that the sum of his distances from the two flag posts is always 10m and the distance between the flag posts is 8m. The equation of the path traced by him is

(A) $\large \frac{x^2}{25} + \frac{y^2}{9} = 1$

(B) $\large \frac{x^2}{4} + \frac{y^2}{1} = 1$

(C) $\large \frac{x^2}{2} + \frac{y^2}{1} = 1$

(D) none of these

Sol. Here 2a = 10 ⇒  a = 5 and 2ae = 8

⇒ e = 8/10 = 4/5

$\large b^2 =  25(1-\frac{16}{25}) = 9 $

⇒  $\large \frac{x^2}{25} + \frac{y^2}{9} = 1$ is equation of the path.