What is the asymptotes of ((x-3)^2)/4-((y+5)^2)/9 =1 ?

The asymptotes of ((x-3)^2)/4-((y+5)^2)/9 =1 is y= 3/2 (x-3)-5,\quad y=-3/2 (x-3)-5

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asymptotes of ((x-3)^2)/4-((y+5)^2)/9 =1

asymptotes

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1

y = \frac{3}{2} (x - 3) - 5, y = - \frac{3}{2} (x - 3) - 5

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 3 ) ^{2}}{4} - \frac{( y + 5 ) ^{2}}{9} = 1 :

Right-left Hyperbola with

(h, k) = (3, - 5), a = 2, b = 3

y = \frac{3}{2} (x - 3) + (- 5), y = - \frac{3}{2} (x - 3) + (- 5)

4 x^{2} - y^{2} - 8 x + 6 y - 4 = 0

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

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

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

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

What is the asymptotes of ((x-3)^2)/4-((y+5)^2)/9 =1 ?
The asymptotes of ((x-3)^2)/4-((y+5)^2)/9 =1 is y= 3/2 (x-3)-5,\quad y=-3/2 (x-3)-5