Find the center and vertices of the hyperbola.
A)center: (-2, -4), vertices: (-2, -6), (-2, -2)
B)center: (2, 4), vertices: (2, 2), (2, 6)
C)center: (2, 4), vertices: (0, 4), (4, 4)
D)center: (-2, -4), vertices: (-4, -4), (0, -4)
E)center: (-4, -2), vertices: (-6, -2), (-2, -2)

Question

Find the center and vertices of the hyperbola. 
A)center: (-2, -4), vertices: (-2, -6), (-2, -2) 
B)center: (2, 4), vertices: (2, 2), (2, 6) 
C)center: (2, 4), vertices: (0, 4), (4, 4) 
D)center: (-2, -4), vertices: (-4, -4), (0, -4) 
E)center: (-4, -2), vertices: (-6, -2), (-2, -2)

Quizplus · Accepted Answer

The standard form for a hyperbola is $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center and $2a$ and $2b$ are the lengths of the transverse and conjugate axes, respectively.

Comparing this to the given equation $\frac{(x-2)^2}{4}-\frac{(y-4)^2}{4}=1$, we see that the center is $(2,4)$ and $a=b=2$. Therefore, the vertices are $(2, 4\pm a)=(2, 2)$ and $(2, 6)$. Thus, the answer is $\boxed{	extbf{(C)}}$.

Find the Center and Vertices of the Hyperbola