the equation of a hyperbola is .
the equations of the asymptotes of the hyperbola are and .

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

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step-by-step explanation: