What is the asymptotes of ((y+2)^2)/4-((x-2)^2)/9 =1 ?

The asymptotes of ((y+2)^2)/4-((x-2)^2)/9 =1 is y= 2/3 (x-2)-2,\quad y=-2/3 (x-2)-2

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asymptotes of ((y+2)^2)/4-((x-2)^2)/9 =1

asymptotes

\frac{( y + 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1

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

Solution steps

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

Calculate Hyperbola properties

\frac{( y + 2 ) ^{2}}{4} - \frac{( x - 2 ) ^{2}}{9} = 1 :

Up-down Hyperbola with

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

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

9 x^{2} - y^{2} + 36 x - 12 y = 36

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

25 y^{2} - 81 x^{2} = 2025

6 x^{2} - 5 y^{2} - 24 x + 10 y - 11 = 0

x^{2} - 4 y^{2} + 2 x + 8 y - 7 = 0

What is the asymptotes of ((y+2)^2)/4-((x-2)^2)/9 =1 ?
The asymptotes of ((y+2)^2)/4-((x-2)^2)/9 =1 is y= 2/3 (x-2)-2,\quad y=-2/3 (x-2)-2