What is the asymptotes of-16x^2+9y^2+96x-90y-63=0 ?

The asymptotes of-16x^2+9y^2+96x-90y-63=0 is y= 4/3 (x-3)+5,\quad y=-4/3 (x-3)+5

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asymptotes of-16x^2+9y^2+96x-90y-63=0

asymptotes

- 16 x^{2} + 9 y^{2} + 96 x - 90 y - 63 = 0

y = \frac{4}{3} (x - 3) + 5, y = - \frac{4}{3} (x - 3) + 5

Solution steps

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

Calculate Hyperbola properties

- 16 x^{2} + 9 y^{2} + 96 x - 90 y - 63 = 0 :

Up-down Hyperbola with

(h, k) = (3, 5), a = 4, b = 3

y = \frac{4}{3} (x - 3) + 5, y = - \frac{4}{3} (x - 3) + 5

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

\frac{x ^{2}}{64} - \frac{y ^{2}}{144} = 1

\frac{x ^{2}}{4} - \frac{y ^{2}}{25} = 1

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

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

What is the asymptotes of-16x^2+9y^2+96x-90y-63=0 ?
The asymptotes of-16x^2+9y^2+96x-90y-63=0 is y= 4/3 (x-3)+5,\quad y=-4/3 (x-3)+5