Answer:
Solution : y = ± 1/3x
Step-by-step explanation:
Remember that the equation of a hyperbola is in the form (y - k)² / a² - (x - h)² / b² = 1. Therefore we have a² here = 9, and b² here = 81.
To determine the asymptotes we can use the equation y = k ± a/b(x - h). What makes this equation really simple, is that k = 0 and h = 0, giving us y = ± a/b(x). Let's isolate a and b given a² = 9, and b² = 81 --- (1)
a² = 9
a = 3
b² = 81
b = 9
Therefore our asymptotes will be in the form y = ± a/b(x) = ± 3/9(x) = ± 1/3x. Our solution is thus option a.
