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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

\frac{x ^{2}}{25} - \frac{y ^{2}}{4} = 1

25 y^{2} - 36 (x - 8)^{2} = 900

\frac{x ^{2}}{25} - \frac{y ^{2}}{49} = 1

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

16 x^{2} - 25 y^{2} = 100

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