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

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

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asymptotes of (x-1)^2-(y+2)^2=1

asymptotes

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

y = x - 3, y = - (x - 1) - 2

Solution steps

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

Calculate Hyperbola properties

(x - 1)^{2} - (y + 2)^{2} = 1 :

Right-left Hyperbola with

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

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

Refine

y = x - 3, y = - (x - 1) - 2

\frac{x ^{2}}{9} - \frac{y ^{2}}{64} = 1

x^{2} - 5 y^{2} = 7

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

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

4 y^{2} - x^{2} = 900

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