Question

A hyperbola centered at the origin has a vertex at (9, 0) and a focus at (−15, 0).

Which are the equations of the asymptotes?

Answer 1

C

Explanation:

Answer 2

Hyperbola equation opening horizontally:

`(x^2)/(a^2) - (y^2)/(b^2) = 1`
Asymptotes:

`y = \pm (b)/(a) x`

'a' is distance vertex is from center --> a = 9
'c' is distance focus is from center --> c = 15

`a^2 + b^2 = c^2 \\ \\ b^2 = 15^2 - 9^2 = 144 \\ \\ b = 12`

Asymptotes are:

`y = \pm (12)/(9) x = \pm (4)/(3) x`