What is the asymptotes of ((y-3)^2)/9-(x^2)/(25)=1 ?

The asymptotes of ((y-3)^2)/9-(x^2)/(25)=1 is y=(3x)/5+3,\quad y=-(3x)/5+3

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asymptotes of ((y-3)^2)/9-(x^2)/(25)=1

asymptotes

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1

y = \frac{3 x}{5} + 3, y = - \frac{3 x}{5} + 3

Solution steps

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

Calculate Hyperbola properties

\frac{( y - 3 ) ^{2}}{9} - \frac{x ^{2}}{25} = 1 :

Up-down Hyperbola with

(h, k) = (0, 3), a = 3, b = 5

y = \frac{3}{5} (x - 0) + 3, y = - \frac{3}{5} (x - 0) + 3

Refine

y = \frac{3 x}{5} + 3, y = - \frac{3 x}{5} + 3

\frac{x ^{2}}{12} - \frac{y ^{2}}{16} = 1

9 y^{2} - 100 x^{2} = 900

x^{2} - 3 y^{2} = 9

2 x^{2} - 2 y^{2} - 20 x + 16 y - 16 = 0

\frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

What is the asymptotes of ((y-3)^2)/9-(x^2)/(25)=1 ?
The asymptotes of ((y-3)^2)/9-(x^2)/(25)=1 is y=(3x)/5+3,\quad y=-(3x)/5+3