What is the asymptotes of ((x+9)^2)/9-((y-8)^2)/4 =1 ?

The asymptotes of ((x+9)^2)/9-((y-8)^2)/4 =1 is y= 2/3 (x+9)+8,\quad y=-2/3 (x+9)+8

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asymptotes of ((x+9)^2)/9-((y-8)^2)/4 =1

asymptotes

\frac{( x + 9 ) ^{2}}{9} - \frac{( y - 8 ) ^{2}}{4} = 1

y = \frac{2}{3} (x + 9) + 8, y = - \frac{2}{3} (x + 9) + 8

Solution steps

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

Calculate Hyperbola properties

\frac{( x + 9 ) ^{2}}{9} - \frac{( y - 8 ) ^{2}}{4} = 1 :

Right-left Hyperbola with

(h, k) = (- 9, 8), a = 3, b = 2

y = \frac{2}{3} (x - (- 9)) + 8, y = - \frac{2}{3} (x - (- 9)) + 8

Refine

y = \frac{2}{3} (x + 9) + 8, y = - \frac{2}{3} (x + 9) + 8

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

9 x^{2} - 16 y^{2} - 18 x + 64 y - 199 = 0

16 y^{2} - 25 x^{2} = 400

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

5 y^{2} - 16 x^{2} + 400 = 0

What is the asymptotes of ((x+9)^2)/9-((y-8)^2)/4 =1 ?
The asymptotes of ((x+9)^2)/9-((y-8)^2)/4 =1 is y= 2/3 (x+9)+8,\quad y=-2/3 (x+9)+8