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

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

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

asymptotes

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

y = 4 (x + 5) + 5, y = - 4 (x + 5) + 5

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

y = 4 (x + 5) + 5, y = - 4 (x + 5) + 5

4 x^{2} - y^{2} - 24 x - 4 y + 28 = 0

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

\frac{x ^{2}}{36} - \frac{y ^{2}}{16} = 1

\frac{x ^{2}}{45} - \frac{y ^{2}}{4} = 1

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

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