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

Question

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

Quizplus · Accepted Answer

The vertices of the hyperbola are the points which lie on the transverse axis and are equidistant from the center. The asymptotes of the hyperbola are the lines which pass through the center of the hyperbola and are perpendicular to the transverse axis. 
By looking at the given options, we can see that option C has the correct values for both vertices and asymptotes. Therefore, the correct choice is C.

Find the Vertices and Asymptotes of the Hyperbola x249−y2100=1\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 100 } = 149x2​−100y2​=1

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