Identify the center and vertices of the hyperbola. $( y - 1 ) ^ { 2 } - ( x + 6 ) ^ { 2 } = 9$
A)center: $( - 6,1 )$ vertices: $( - 6 , - 2 ) , ( - 6,4 )$
B)center: $( 6 , - 1 )$ vertices: $( - 6,3 ) , ( - 6 , - 3 )$
C)center: $( 6 , - 1 )$ vertices: $( 3 , - 1 ) , ( 9 , - 1 )$
D)center: $( - 6,1 )$ vertices: $( - 9,1 ) , ( - 3,1 )$
E)center: $( - 6,1 )$ vertices: $( - 6,3 ) , ( - 6 , - 3 )$

Question

Quizplus · Accepted Answer

The center of the hyperbola is found by setting the inside of the parentheses to zero, giving $(-6, 1)$. The vertices are along the y-axis (since $y$ is positive in the equation) and are a distance of 3 (the square root of 9) from the center, giving $(-6, -2)$ and $(-6, 4)$.

Identify the Center and Vertices of the Hyperbola (y−1)2−(x+6)2=9( y - 1 ) ^ { 2 } - ( x + 6 ) ^ { 2 } = 9(y−1)2−(x+6)2=9

Identify the Center and Vertices of the Hyperbola $( y - 1 ) ^ { 2 } - ( x + 6 ) ^ { 2 } = 9$