What is the asymptotes of ((x-1)^2)/9-((y+6)^2)/4 =1 ?

The asymptotes of ((x-1)^2)/9-((y+6)^2)/4 =1 is y= 2/3 (x-1)-6,\quad y=-2/3 (x-1)-6

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asymptotes of ((x-1)^2)/9-((y+6)^2)/4 =1

asymptotes

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 6 ) ^{2}}{4} = 1

y = \frac{2}{3} (x - 1) - 6, y = - \frac{2}{3} (x - 1) - 6

Solution steps

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

Calculate Hyperbola properties

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 6 ) ^{2}}{4} = 1 :

Right-left Hyperbola with

(h, k) = (1, - 6), a = 3, b = 2

y = \frac{2}{3} (x - 1) + (- 6), y = - \frac{2}{3} (x - 1) + (- 6)

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

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

\frac{x ^{2}}{36} - \frac{y ^{2}}{25} = 1

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

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

What is the asymptotes of ((x-1)^2)/9-((y+6)^2)/4 =1 ?
The asymptotes of ((x-1)^2)/9-((y+6)^2)/4 =1 is y= 2/3 (x-1)-6,\quad y=-2/3 (x-1)-6