Solve the Problem $5 x ^ { 2 } - y ^ { 2 } = 31$

Multiple Choice

Solve the problem.
-A system for tracking ships indicated that a ship lies on a hyperbolic path described by $5 x ^ { 2 } - y ^ { 2 } = 31$ . The process is repeated and the ship is found to lie on a hyperbolic path described by $y ^ { 2 } - 3 x ^ { 2 } = 1$ . If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location.

A) $( 4,7 )$
B) $( - 4 , - 7 )$
C) $( 7,4 )$
D) $( - 7 , - 4 )$