Question

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

Answer 1

3rd graph is the correct graph

Explanation:

Given is the equation of hyperbola as

`y = ± √(x^2-5)`

Square both sides and rearrange to get

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

Vertices are
`(√(5) ,0) \\(-√(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.