Question

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

Answer 1

Answer:

C

Step-by-step explanation:

Answer 2

Hyperbola equation opening horizontally:
$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$
Asymptotes:
$y = \pm \frac{b}{a} x$

'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:
$y = \pm \frac{12}{9} x = \pm \frac{4}{3} x$