What is the asymptotes of ((x+2)^2)/(36)-y^2=1 ?

The asymptotes of ((x+2)^2)/(36)-y^2=1 is y= 1/6 (x+2),\quad y=-1/6 (x+2)

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asymptotes of ((x+2)^2)/(36)-y^2=1

asymptotes

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1

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

Solution steps

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

Calculate Hyperbola properties

\frac{( x + 2 ) ^{2}}{36} - y^{2} = 1 :

Right-left Hyperbola with

(h, k) = (- 2, 0), a = 6, b = 1

y = \frac{1}{6} (x - (- 2)) + 0, y = - \frac{1}{6} (x - (- 2)) + 0

Refine

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

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

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

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

x = x^{2} - \frac{y ^{2}}{9}

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

What is the asymptotes of ((x+2)^2)/(36)-y^2=1 ?
The asymptotes of ((x+2)^2)/(36)-y^2=1 is y= 1/6 (x+2),\quad y=-1/6 (x+2)