Solve the problem.
-The hyperbola $\frac { x ^ { 2 } } { 7 } - \frac { y ^ { 2 } } { 3 } = 1$ is shifted up 5 units and left 8 units. Find an equation for the new hyperbola and find the new vertices.
A) $\frac { ( x + 8 ) ^ { 2 } } { 7 } - \frac { ( y - 5 ) ^ { 2 } } { 3 } = 1$; vertices: $( - 8 \pm \sqrt { 7 } , 5 )$
B) $\frac { ( x + 5 ) ^ { 2 } } { 7 } - \frac { ( y - 8 ) ^ { 2 } } { 3 } = 1$; vertices: $( - 8,5 \pm \sqrt { 3 } )$
C) $\frac { ( x + 8 ) ^ { 2 } } { 7 } - \frac { ( y - 5 ) ^ { 2 } } { 3 } = 1$; vertices: $( - 8,5 \pm \sqrt { 3 } )$
D) $\frac { ( x - 8 ) ^ { 2 } } { 7 } - \frac { ( y + 5 ) ^ { 2 } } { 3 } = 1 ;$ vertices: $( - 8 \pm \sqrt { 7 } , 5 )$

Question

Quizplus · Accepted Answer

The correct answer is A because the hyperbola is shifted up 5 units and left 8 units, so the new equation is $\frac { ( x + 8 ) ^ { 2 } } { 7 } - \frac { ( y - 5 ) ^ { 2 } } { 3 } = 1$. The new vertices are $( - 8 \pm \sqrt { 7 } , 5 )$.

Solve the Problem x27−y23=1\frac { x ^ { 2 } } { 7 } - \frac { y ^ { 2 } } { 3 } = 17x2​−3y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 7 } - \frac { y ^ { 2 } } { 3 } = 1$