What is the asymptotes of 16x^2-9y^2=144 ?

The asymptotes of 16x^2-9y^2=144 is y=(4x)/3 ,\quad y=-(4x)/3

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asymptotes of 16x^2-9y^2=144

asymptotes

16 x^{2} - 9 y^{2} = 144

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

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 9 y^{2} = 144 :

Right-left Hyperbola with

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

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

Refine

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

y^{2} = - 9 x

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

\frac{x ^{2}}{64} - \frac{y ^{2}}{36} = 1

x^{2} + y^{2} - 6 x + 2 y + 9 = 0

4 x^{2} + y^{2} = 16

What is the asymptotes of 16x^2-9y^2=144 ?
The asymptotes of 16x^2-9y^2=144 is y=(4x)/3 ,\quad y=-(4x)/3