What is the asymptotes of 16x^2-9y^2-96x+288=0 ?

The asymptotes of 16x^2-9y^2-96x+288=0 is y= 4/3 (x-3),\quad y=-4/3 (x-3)

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asymptotes of 16x^2-9y^2-96x+288=0

asymptotes

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

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

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 9 y^{2} - 96 x + 288 = 0 :

Up-down Hyperbola with

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

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

Refine

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

10 x^{2} - 25 y^{2} = 100

(x - 4)^{2} - (y + 1)^{2} = 25

- 9 x^{2} + 8 y^{2} + 36 x + 48 y = 36

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

5 x^{2} - 4 y^{2} - 20 x - 8 y = 4

What is the asymptotes of 16x^2-9y^2-96x+288=0 ?
The asymptotes of 16x^2-9y^2-96x+288=0 is y= 4/3 (x-3),\quad y=-4/3 (x-3)