Identify the vertices and asymptotes of the hyperbola. $x ^ { 2 } - y ^ { 2 } = 36$
A)vertices: $( 6 , - 6 ) , ( 6,6 )$ asymptotes: $y = - 6 x , y = \frac { x } { 6 }$
B)vertices: $( - 36,0 ) , ( 36,0 )$ asymptotes: $y = - x , y = x$
C)vertices: $( 0 , - 6 ) , ( 0,6 )$ asymptotes: $y = - 6 x , y = \frac { x } { 6 }$
D)vertices: $( - 6,0 ) , ( 6,0 )$ asymptotes: $y = - x , y = x$
E)vertices: $( 0 , - 6 ) , ( 0,6 )$ asymptotes: $y = - x , y = x$

Question

Quizplus · Accepted Answer

We can rewrite the hyperbola as $\frac{x^2}{6^2}-\frac{y^2}{6^2}=1$. This tells us that $a=6$ and $b=6$. Therefore, the vertices are located at $(\pm6,0)$. The asymptotes have slopes $\pm\frac{b}{a}=\pm1$, so their equations are $y=\pm x$. Therefore, the correct choice is (D).

Identify the Vertices and Asymptotes of the Hyperbola x2−y2=36x ^ { 2 } - y ^ { 2 } = 36x2−y2=36

Identify the Vertices and Asymptotes of the Hyperbola $x ^ { 2 } - y ^ { 2 } = 36$