Describe the hyperbola which is the graph of the equation $\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 1$ .
A) center: $( 0 , - 4 )$ ; vertices: $( 0,3 )$ , $( 0 , - 3 )$
B) center: $( - 4,0 )$ ; vertices: $( - 4,3 )$ , $( - 4 , - 3 )$
C) center: $( 4,0 )$ ; vertices: $( 4,3 )$ , $( 4 , - 3 )$
D) center: $( - 4,0 )$ ; vertices: $( 0,7 )$ , $( 0,4 )$

Question

Quizplus · Accepted Answer

The equation is in the form $\frac{y^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$, indicating a hyperbola centered at $(h, k)$ with vertices along the y-axis. Here, $h = -4$ and $k = 0$, making the center $(-4, 0)$. The distance from the center to the vertices along the y-axis is $a = 3$, so the vertices are $(-4, 3)$ and $(-4, -3)$.

Describe the Hyperbola Which Is the Graph of the Equation y29−(x+4)249=1\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 19y2​−49(x+4)2​=1

Describe the Hyperbola Which Is the Graph of the Equation $\frac { y ^ { 2 } } { 9 } - \frac { ( x + 4 ) ^ { 2 } } { 49 } = 1$