Use vertices and asymptotes to graph the hyperbola. find the equations of the asymptotes.

y = ± square root of x^2 - 5

a. asymptotes: y = ± x
b. asymptotes: y = ± 5/3 x
c. asymptotes: y = ± 5/3 x
d. asymptotes: y = ± x

Based on the given graphs and options above, the correct answer would be option D. So using the vertices and the asymptotes to graph the hyperbola, the equations of the of the asymptotes y = ± square root of x^2 - 5 would be this: Asymptotes: y = ± x.  It is y^2=x^2−5, x^2−y^2=5; asymptotes are y = ± x and it's a horizontal hyperbola. Hope this answer helps.