Identify the vertices and asymptotes of the hyperbola. $y ^ { 2 } - x ^ { 2 } = 4$
A)vertices: $( 0 , - 2 ) , ( 0,2 )$ asymptotes: $y = - x , y = x$
B)vertices: $( - 4,0 ) , ( 4,0 )$ asymptotes: $y = - x , y = x$
C)vertices: $( - 2,0 ) , ( 2,0 )$ asymptotes: $y = - x , y = x$
D)vertices: $( - 2,2 ) , ( 2,2 )$ asymptotes: $y = - 2 x , y = \frac { x } { 2 }$
E)vertices: $( 0 , - 2 ) , ( 0,2 )$ asymptotes: $y = - 2 x , y = \frac { x } { 2 }$

Question

Quizplus · Accepted Answer

The given equation $y^2 - x^2 = 4$ can be rewritten in standard form as $\frac{y^2}{2^2} - \frac{x^2}{2^2} = 1$, indicating a hyperbola centered at the origin (0,0) with vertices along the y-axis at $(0, \pm2)$ and asymptotes given by $y = \pm x$, matching choice A.

Identify the Vertices and Asymptotes of the Hyperbola y2−x2=4y ^ { 2 } - x ^ { 2 } = 4y2−x2=4

Identify the Vertices and Asymptotes of the Hyperbola $y ^ { 2 } - x ^ { 2 } = 4$