What is the asymptotes of-(x^2}{16}+\frac{y^2)/9 =1 ?

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

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

asymptotes

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

4 x^{2} - y^{2} + 16 x + 6 y = 9

9 x^{2} - 25 y^{2} - 72 x + 369 = 0

6 x^{2} - \frac{2}{3} y^{2} = 4

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

\frac{x ^{2}}{4} - \frac{y ^{2}}{16} = 1

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