Graph Hyperbolas Not Centered at the Origin
-$$( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$$
A) Center: $( - 2,3 )$; Vertices: $( - 10,3 )$ and $( 6,3 )$; Foci: $( - 2 - \sqrt { 65 } , 3 )$ and $( - 2 + \sqrt { 65 } , 3 )$
B) Center: $( 2 , - 3 )$; Vertices: $( - 6 , - 3 )$ and $( 10 , - 3 )$; Foci: $( 2 - \sqrt { 65 } , 3 )$ and $( 2 + \sqrt { 65 } , 3 )$
C) Center: $( - 2,3 )$; Vertices: $( - 9,4 )$ and $( 7,4 )$; Foci: $( - 1 - \sqrt { 65 } , 4 )$ and $( - 1 + \sqrt { 65 } , 4 )$
D) Center: $( - 2,3 )$; Vertices: $( 8,3 )$ and $( - 8,3 )$; Foci: $( - \sqrt { 65 } , 3 )$ and $( \sqrt { 65 } , 3 )$

Question

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1$, where $(h, k)$ is the center. Here, it's $(x + 2)^2 / 64 - (y - 3)^2 / 1 = 1$, indicating the center is $(-2, 3)$. The vertices are along the x-axis from the center, $\pm 8$ units away, making them $(-10, 3)$ and $(6, 3)$. The foci are calculated using $c^2 = a^2 + b^2$, giving $c = \sqrt{65}$, so the foci are $(-2 - \sqrt{65}, 3)$ and $(-2 + \sqrt{65}, 3)$.

Graph Hyperbolas Not Centered at the Origin - (x+2)2−64(y−3)2=64( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64(x+2)2−64(y−3)2=64

Graph Hyperbolas Not Centered at the Origin
- $( x + 2 ) ^ { 2 } - 64 ( y - 3 ) ^ { 2 } = 64$