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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

x^{2} - 4 y^{2} = 16

x^{2} - 9 y^{2} - 4 x + 36 y - 41 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{324} = 1

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