Two listening posts, A and B are 500m apart. An explosion is heard at these posts. From the difference in times it is determined that the site of explosion is 800m closer to A then to B. If the site of explosion lies on a hyperbolic curve, then the equation of the hyperbola is --

A \( \frac{x^{2}}{\left ( 400 \right )^{2}} - \frac{y^{2}}{\left ( 5000 \right )^{2}} = 1 \)

B \( \frac{x^{2}}{\left ( 400 \right )^{2}} - \frac{y^{2}}{\left ( 2468 \right )^{2}} = 1 \)

C \( \frac{x^{2}}{\left ( 8000 \right )^{2}} - \frac{y^{2}}{\left ( 2500 \right )^{2}} = 1 \)

D None

Correct Answer: Option D