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

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

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

asymptotes

\frac{y ^{2}}{9} - \frac{x ^{2}}{16} = 1

y = \frac{3 x}{4}, y = - \frac{3 x}{4}

Solution steps

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

Calculate Hyperbola properties

\frac{y ^{2}}{9} - \frac{x ^{2}}{16} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 3, b = 4

y = \frac{3}{4} (x - 0) + 0, y = - \frac{3}{4} (x - 0) + 0

Refine

y = \frac{3 x}{4}, y = - \frac{3 x}{4}

x = 3 y^{2}

3 y^{2} = 24 x

f (x) = x^{2} - 6 x

y^{2} + 12 x + 4 y - 32 = 0

x^{2} + y^{2} - 18 x - 14 y + 124 = 0

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