Identify the vertices and asymptotes of the hyperbola. $x^2-y^2=36$

A) vertices: $(6,-6),(6,6)$ asymptotes: $y=-6x,y=\frac{x}{6}$
B) vertices: $(-36,0),(36,0)$ asymptotes: $y=-x,y=x$
C) vertices: $(0,-6),(0,6)$ asymptotes: $y=-6x,y=\frac{x}{6}$
D) vertices: $(-6,0),(6,0)$ asymptotes: $y=-x,y=x$
E) vertices: $(0,-6),(0,6)$ asymptotes: $y=-x,y=x$

Vertices

The plural of vertex, referring to the corners or intersecting points of geometric shapes or graphs.

Hyperbola

A type of smooth curve lying in a plane, consisting of two branches, which are mirror images of each other, and asymptotically approaching fixed lines.

Asymptotes

Asymptotes are lines that a graph approaches but never reaches, illustrating behavior towards infinity or certain points within the domain.