Question

Which equations represent the asymptotes of the hyperbola?

Answer 1

Answer:

  see below

Step-by-step explanation:

The equation of the hyperbola can be written as ...

  ((x -h)/a)² -((y -k)/b)² = 1

This has asymptotes ...

  (x -h)/a ± (y -k)/b = 0

Solving for y, we have ...

  y = ±(b/a)(x -h) +k

Filling in the given values a=6, b=8, h=1, k=2, we have ...

  y = ±8/6(x -1) +2

  $y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}$