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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

(h, k) = (2, 0), a = 2, b = 3

y = \frac{3}{2} (x - 2) + 0, y = - \frac{3}{2} (x - 2) + 0

Refine

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

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

- 9 x^{2} + 16 y^{2} - 90 x + 32 y - 353 = 0

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

\frac{y ^{2}}{12} - \frac{x ^{2}}{16} = 1

y^{2} - x^{2} = 22

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