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

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

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

asymptotes

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

y = \frac{3}{2} (x + 2) - 4, y = - \frac{3}{2} (x + 2) - 4

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (- 2, - 4), a = 3, b = 2

y = \frac{3}{2} (x - (- 2)) + (- 4), y = - \frac{3}{2} (x - (- 2)) + (- 4)

Refine

y = \frac{3}{2} (x + 2) - 4, y = - \frac{3}{2} (x + 2) - 4

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

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

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

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

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

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