What is the asymptotes of 16x^2-9y^2+32x+72y-704=0 ?

The asymptotes of 16x^2-9y^2+32x+72y-704=0 is y=(4(x+1))/3+4,\quad y=-(4(x+1))/3+4

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asymptotes of 16x^2-9y^2+32x+72y-704=0

asymptotes

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

y = \frac{4 ( x + 1 )}{3} + 4, y = - \frac{4 ( x + 1 )}{3} + 4

Solution steps

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

Calculate Hyperbola properties

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0 :

Right-left Hyperbola with

(h, k) = (- 1, 4), a = 6, b = 8

y = \frac{8}{6} (x - (- 1)) + 4, y = - \frac{8}{6} (x - (- 1)) + 4

Refine

y = \frac{4 ( x + 1 )}{3} + 4, y = - \frac{4 ( x + 1 )}{3} + 4

- 9 x^{2} + 16 y^{2} - 90 x + 128 y - 113 = 0

5 (y + 3)^{2} - 4 (x - 1)^{2} = 20

\frac{x ^{2}}{144} - \frac{y ^{2}}{25} = 1

36 x^{2} - y^{2} = 36

36 x^{2} - 25 y^{2} = 900

What is the asymptotes of 16x^2-9y^2+32x+72y-704=0 ?
The asymptotes of 16x^2-9y^2+32x+72y-704=0 is y=(4(x+1))/3+4,\quad y=-(4(x+1))/3+4