Find the vertices and foci of the hyperbola.
-$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$$
A) Vertices: $( \pm 2,0 )$; Foci: $( \pm 4,0 )$
B) Vertices: $( \pm 4,0 )$; Foci: $( \pm 2,0 )$
C) Vertices: $( 0 , \pm 4 )$; Foci: $( 0 , \pm 2 )$
D) Vertices: $( 0 , \pm 2 )$; Foci: $( 0 , \pm 4 )$

Question

Quizplus · Accepted Answer

The given equation $\frac{x^2}{4} - \frac{y^2}{12} = 1$ represents a hyperbola centered at the origin with its major axis along the x-axis. The vertices are located at $\pm a, 0$, where $a^2 = 4$, so $a = 2$, giving vertices at $(\pm 2, 0)$. The foci are located at $\pm c, 0$, where $c^2 = a^2 + b^2$ and $b^2 = 12$, so $c^2 = 4 + 12 = 16$, giving $c = 4$ and foci at $(\pm 4, 0)$.

Find the Vertices and Foci of the Hyperbola x24−y212=1\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 14x2​−12y2​=1

Find the Vertices and Foci of the Hyperbola $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 12 } = 1$