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

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

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

asymptotes

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

y = 2 (x - 1) + 2, y = - 2 (x - 1) + 2

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

y = 2 (x - 1) + 2, y = - 2 (x - 1) + 2

4 x^{2} - 9 y^{2} - 36 < 0

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

9 y^{2} - 16 x^{2} = 144

(x - 5)^{2} - (y - 4)^{2} = 1

x^{2} - 4 y^{2} - 20 x - 64 y - 172 = 0

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