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

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

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

asymptotes

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

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

Right-left Hyperbola with

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

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

y^{2} - x^{2} = 1

16 y^{2} - 32 y - 9 x^{2} - 18 x = 137

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

9 y^{2} - 36 x^{2} = 324

\frac{y ^{2}}{25} - \frac{x ^{2}}{81} = 1

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