What is the asymptotes of 1/4 (y+5)^2-1/16 (x+1)^2=1 ?

The asymptotes of 1/4 (y+5)^2-1/16 (x+1)^2=1 is y=(x+1)/2-5,\quad y=-(x+1)/2-5

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asymptotes of 1/4 (y+5)^2-1/16 (x+1)^2=1

asymptotes

\frac{1}{4} (y + 5)^{2} - \frac{1}{16} (x + 1)^{2} = 1

y = \frac{x + 1}{2} - 5, y = - \frac{x + 1}{2} - 5

Solution steps

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

Calculate Hyperbola properties

\frac{1}{4} (y + 5)^{2} - \frac{1}{16} (x + 1)^{2} = 1 :

Up-down Hyperbola with

(h, k) = (- 1, - 5), a = 2, b = 4

y = \frac{2}{4} (x - (- 1)) + (- 5), y = - \frac{2}{4} (x - (- 1)) + (- 5)

Refine

y = \frac{x + 1}{2} - 5, y = - \frac{x + 1}{2} - 5

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

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

What is the asymptotes of 1/4 (y+5)^2-1/16 (x+1)^2=1 ?
The asymptotes of 1/4 (y+5)^2-1/16 (x+1)^2=1 is y=(x+1)/2-5,\quad y=-(x+1)/2-5