What is the asymptotes of ((y-2)^2)/9-(x+2)^2=1 ?

The asymptotes of ((y-2)^2)/9-(x+2)^2=1 is y=3(x+2)+2,\quad y=-3(x+2)+2

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asymptotes of ((y-2)^2)/9-(x+2)^2=1

asymptotes

\frac{( y - 2 ) ^{2}}{9} - (x + 2)^{2} = 1

y = 3 (x + 2) + 2, y = - 3 (x + 2) + 2

Solution steps

y = \pm \frac{a}{b} (x - h) + k

Calculate Hyperbola properties

\frac{( y - 2 ) ^{2}}{9} - (x + 2)^{2} = 1 :

Up-down Hyperbola with

(h, k) = (- 2, 2), a = 3, b = 1

y = \frac{3}{1} (x - (- 2)) + 2, y = - \frac{3}{1} (x - (- 2)) + 2

Refine

y = 3 (x + 2) + 2, y = - 3 (x + 2) + 2

2 x^{2} - 3 y^{2} = 6

6 x^{2} - 36 y^{2} = 2304

9 y^{2} - 16 x^{2} - 256 = 0

- 9 x^{2} + y^{2} = 36

y^{2} = x^{2} - 1

What is the asymptotes of ((y-2)^2)/9-(x+2)^2=1 ?
The asymptotes of ((y-2)^2)/9-(x+2)^2=1 is y=3(x+2)+2,\quad y=-3(x+2)+2