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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

- 9 x^{2} + 16 y^{2} - 90 x + 128 y - 113 = 0

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

\frac{x ^{2}}{144} - \frac{y ^{2}}{25} = 1

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

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