Identify the vertices and asymptotes of the hyperbola. $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1$
A)vertices: $( - 10,0 ) , ( 10,0 )$ asymptotes: $y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x$
B)vertices: $( - 10,0 ) , ( 10,0 )$ asymptotes: $y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x$
C)vertices: $( 0 , - 7 ) , ( 0,7 )$ asymptotes: $y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x$
D)vertices: $( 0 , - 10 ) , ( 0,10 )$ asymptotes: $y = - \frac { 7 } { 10 } x , y = \frac { 7 } { 10 } x$
E)vertices: $( - 7,0 ) , ( 7,0 )$ asymptotes: $y = - \frac { 10 } { 7 } x , y = \frac { 10 } { 7 } x$

Question

Quizplus · Accepted Answer

The given equation $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1$ represents a hyperbola with a vertical transverse axis. The vertices are found at $(0, \pm \sqrt{49})$, which simplifies to $(0, \pm 7)$. The asymptotes for a hyperbola of the form $\frac { y ^ { 2 } } { a^2 } - \frac { x ^ { 2 } } { b^2 } = 1$ are given by $y = \pm \frac { a } { b } x$, which in this case simplifies to $y = \pm \frac { 7 } { 10 } x$.

Identify the Vertices and Asymptotes of the Hyperbola y249−x2100=1\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 149y2​−100x2​=1

Identify the Vertices and Asymptotes of the Hyperbola $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 100 } = 1$