Solve the problem.
-The hyperbola $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 144 } = 1$ is shifted horizontally and vertically to obtain the hyperbola $\frac { ( x - 1 ) ^ { 2 } } { 81 } - \frac { ( y + 3 ) ^ { 2 } } { 144 } = 1$ Find the foci of the new hyperbola.
A) (-14, -3), (16, -3)
B) (-11, -3), (13, -3)
C) (-3, -14), (-3, 16)
D) (-3, -11), (-3, 13)

Question

Quizplus · Accepted Answer

The center of the new hyperbola is (1, -3). The distance from the center to the foci is $c = \sqrt { a ^ { 2 } + b ^ { 2 } } = \sqrt { 81 + 144 } = 15$. So the foci are (-14, -3) and (16, -3).

Solve the Problem x281−y2144=1\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 144 } = 181x2​−144y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 144 } = 1$