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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

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

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

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

16 x^{2} - y^{2} = 256

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

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