Answer:
y = 3(x + 2) + 2 and y = -3(x + 2) + 2
Step-by-step explanation:
* Lets revise the equation of the hyperbola with center (h , k) and
transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1
- The coordinates of the vertices are (h , k ± a)
- The coordinates of the co-vertices are (h ± b , k)
- The coordinates of the foci are (h , k ± c) where c² = a² + b²
- The equations of the asymptotes are ± a/b (x - h) + k
* Lets solve the problem
∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1
∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1
∴ h = -2 , k = 2
∴ a² = 9
∴ a = √9 = 3
∴ b² = 1
∴ b = √1 = 1
∵ The equations of the asymptotes are y = ± a/b (x - h) + k
∴ The equations of the asymptotes are y = ± 3/1 (x - -2) + 2
∴ The equations of the asymptotes are y = ± 3 (x + 2) + 2
* The equations of the asymptotes of the hyperbola are
y = 3(x + 2) + 2 and y = -3(x + 2) + 2
