If $\mathrm { P } ( 10,2 \sqrt { 15 } )$ lies on hyperbola $\frac { \mathrm { x } ^ { 2 } } { \mathrm { a } ^ { 2 } } - \frac { \mathrm { y } ^ { 2 } } { \mathrm {~b} ^ { 2 } } = 1$ and length of latus rectum $= 8$, then the square of area of $\triangle \mathrm { PS } _ { 1 } \mathrm {~S} _ { 2 }$ is [where $S _ { 1 } \& S _ { 2 }$ are the focii of the hyperbola]
(A) 2700
(B) 1750
(C) 2400
(D) 3600