Solve Problems Using Systems of Nonlinear Equations
-A system for tracking ships indicated that a ship lies on a hyperbolic path described by $6 \mathrm { x } ^ { 2 } - \mathrm { y } ^ { 2 } = 18$. The process is repeated and the ship is found to lie on a hyperbolic path described by $y ^ { 2 } - 3 x ^ { 2 } = 9$. If it is known that the ship is located in the first quadrant of the coordinate system, determine its exact location.
A) $( 3,6 )$
B) $( - 3 , - 6 )$
C) $( 6,3 )$
D) $( - 6 , - 3 )$

Question

Quizplus · Accepted Answer

To find the ship's location, we solve the system of nonlinear equations:1. $6x^2 - y^2 = 18$2. $y^2 - 3x^2 = 9$Adding both equations to eliminate $y^2$, we get:$$6x^2 - y^2 + y^2 - 3x^2 = 18 + 9$$$$3x^2 = 27$$$$x^2 = 9$$$$x = 3$$ (since the ship is in the first quadrant, $x > 0$)Substituting $x = 3$ into the second equation:$$y^2 - 3(3)^2 = 9$$$$y^2 - 27 = 9$$$$y^2 = 36$$$$y = 6$$ (since the ship is in the first quadrant, $y > 0$)Therefore, the ship's location is $(3, 6)$.

Solve Problems Using Systems of Nonlinear Equations -A System for Tracking

Solve Problems Using Systems of Nonlinear Equations
-A System for Tracking