Question

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

Answer 1

Answer:

3rd graph is the correct graph

Step-by-step explanation:

Given is the equation of hyperbola as

$y = ± \sqrt{x^2-5}$

Square both sides and rearrange to get

$y^2=x^2-5 \\x^2-y^2 =5$

Vertices are $(\sqrt{5} ,0) \\(-\sqrt{5} ,0)$

Asymptotes would have the same equation as hyperbola except constant term as 0

$x^2-y^2 =0$

are the asymptotes

Or $y = ± x$ option d is right.

Answer 2

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.