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

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

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

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (- 1, 0), a = 1, b = 2

y = \frac{1}{2} (x - (- 1)) + 0, y = - \frac{1}{2} (x - (- 1)) + 0

Refine

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

x^{2} - 4 y^{2} - 8 = 0

4 y^{2} - x^{2} + 40 y - 4 x + 60 = 0

16 x^{2} - y^{2} = 256

\frac{( x - 2 ) ^{2}}{4} - \frac{y ^{2}}{9} = 1

\frac{y ^{2}}{16} - \frac{x ^{2}}{16} = 1

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