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

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

Popular >

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

asymptotes

(x - 2)^{2} - \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

(x - 2)^{2} - \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}}{16} - \frac{x ^{2}}{256} = 1

x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0

\frac{y ^{2}}{4} - \frac{x ^{2}}{36} = 1

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

4 y^{2} - 5 x^{2} - 48 y - 10 x + 59 = 0

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