Solve the problem.
-The hyperbola $\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 64 } = 1$ is shifted horizontally and vertically to obtain the hyperbola $\frac { ( x + 5 ) ^ { 2 } } { 100 } - \frac { ( y + 2 ) ^ { 2 } } { 64 } = 1$ Find the center and vertices of the new hyperbola.
A) Center: (-2, -5); Vertices: (-2, -15), (-2, 5)
B) Center: (-2, -5); Vertices: (-15, -2), (5, -2)
C) Center: (-5, -2); Vertices: (-15, -2), (5, -2)
D) Center: (-5, -2); Vertices: (-2, -15), (-2, 5)

Question

Quizplus · Accepted Answer

Comparing the given equation with the standard form of a hyperbola, we get:
Center of the original hyperbola: (0,0)
a = 10
b = 8
Vertices: (-10,0), (10,0), (0,-8), (0,8)

After shifting the hyperbola horizontally and vertically, we get:
Center of the shifted hyperbola: (-5,-2)
a = 10
b = 8
Vertices: (-15,-2), (5,-2), (-5,-10), (-5,6)

Hence, the correct choice is C.

Solve the Problem x2100−y264=1\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 64 } = 1100x2​−64y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 100 } - \frac { y ^ { 2 } } { 64 } = 1$