Solve the problem.
-The hyperbola $\frac { x ^ { 2 } } { 5 } - \frac { y ^ { 2 } } { 16 } = 1$ is shifted down 8 units and right 2 units. Find an equation for the new hyperbola and find the new center.
A) $\frac { ( x + 2 ) ^ { 2 } } { 5 } - \frac { ( y - 8 ) ^ { 2 } } { 11 } = 1$; center: $( 2 , - 8 )$
B) $\frac { ( x - 8 ) ^ { 2 } } { 5 } + \frac { ( y + 2 ) ^ { 2 } } { 11 } = 1 ;$ center: $( - 8,2 )$
C) $\frac { ( x - 2 ) ^ { 2 } } { 5 } - \frac { ( y + 8 ) ^ { 2 } } { 16 } = 1$; center: $( 2 , - 8 )$
D) $\frac { ( x + 8 ) ^ { 2 } } { 5 } - \frac { ( y - 2 ) ^ { 2 } } { 11 } = 1$; center: $( 8 , - 2 )$

Question

Quizplus · Accepted Answer

Shifting the hyperbola right 2 units and down 8 units results in replacing $x$ with $x-2$ and $y$ with $y+8$, without changing the denominators. The new center is $(2, -8)$.

Solve the Problem x25−y216=1\frac { x ^ { 2 } } { 5 } - \frac { y ^ { 2 } } { 16 } = 15x2​−16y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 5 } - \frac { y ^ { 2 } } { 16 } = 1$