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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Right-left Hyperbola with

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

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

Refine

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

\frac{y ^{2}}{4} - \frac{x ^{2}}{25} = 1

\frac{x ^{2}}{3} - \frac{y ^{2}}{3} = 1

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

- 16 x^{2} + 9 y^{2} + 96 x - 90 y - 63 = 0

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

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