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

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

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asymptotes of ((y-2)^2)/4-((x+3)^2)/9 =1

asymptotes

\frac{( y - 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1

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

Solution steps

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

Calculate Hyperbola properties

\frac{( y - 2 ) ^{2}}{4} - \frac{( x + 3 ) ^{2}}{9} = 1 :

Up-down Hyperbola with

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

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

Refine

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

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0

y^{2} = x^{2} - 4 x

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

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