What is the asymptotes of-9x^2+16y^2-90x+128y-113=0 ?

The asymptotes of-9x^2+16y^2-90x+128y-113=0 is y= 3/4 (x+5)-4,\quad y=-3/4 (x+5)-4

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asymptotes of-9x^2+16y^2-90x+128y-113=0

asymptotes

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

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

Solution steps

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

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

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

Refine

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

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

x^{2} - y^{2} + 7 x + 8 y = 5

What is the asymptotes of-9x^2+16y^2-90x+128y-113=0 ?
The asymptotes of-9x^2+16y^2-90x+128y-113=0 is y= 3/4 (x+5)-4,\quad y=-3/4 (x+5)-4