What is the asymptotes of ((y+3)^2)/9-((x-2)^2)/(16)=1 ?

The asymptotes of ((y+3)^2)/9-((x-2)^2)/(16)=1 is y= 3/4 (x-2)-3,\quad y=-3/4 (x-2)-3

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asymptotes of ((y+3)^2)/9-((x-2)^2)/(16)=1

asymptotes

\frac{( y + 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1

y = \frac{3}{4} (x - 2) - 3, y = - \frac{3}{4} (x - 2) - 3

Solution steps

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

Calculate Hyperbola properties

\frac{( y + 3 ) ^{2}}{9} - \frac{( x - 2 ) ^{2}}{16} = 1 :

Up-down Hyperbola with

(h, k) = (2, - 3), a = 3, b = 4

y = \frac{3}{4} (x - 2) + (- 3), y = - \frac{3}{4} (x - 2) + (- 3)

y^{2} - 10 y - 12 x + 37 = 0

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1

f (x) = x^{2} - 2 x

\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1

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

What is the asymptotes of ((y+3)^2)/9-((x-2)^2)/(16)=1 ?
The asymptotes of ((y+3)^2)/9-((x-2)^2)/(16)=1 is y= 3/4 (x-2)-3,\quad y=-3/4 (x-2)-3