What is the asymptotes of-9x^2+16y^2-90x+32y-353=0 ?

The asymptotes of-9x^2+16y^2-90x+32y-353=0 is y= 3/4 (x+5)-1,\quad y=-3/4 (x+5)-1

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asymptotes of-9x^2+16y^2-90x+32y-353=0

asymptotes

- 9 x^{2} + 16 y^{2} - 90 x + 32 y - 353 = 0

y = \frac{3}{4} (x + 5) - 1, y = - \frac{3}{4} (x + 5) - 1

Solution steps

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

Calculate Hyperbola properties

- 9 x^{2} + 16 y^{2} - 90 x + 32 y - 353 = 0 :

Up-down Hyperbola with

(h, k) = (- 5, - 1), a = 3, b = 4

y = \frac{3}{4} (x - (- 5)) + (- 1), y = - \frac{3}{4} (x - (- 5)) + (- 1)

Refine

y = \frac{3}{4} (x + 5) - 1, y = - \frac{3}{4} (x + 5) - 1

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

\frac{y ^{2}}{12} - \frac{x ^{2}}{16} = 1

y^{2} - x^{2} = 22

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

9 x^{2} - y^{2} - 54 x - 2 y + 71 = 0

What is the asymptotes of-9x^2+16y^2-90x+32y-353=0 ?
The asymptotes of-9x^2+16y^2-90x+32y-353=0 is y= 3/4 (x+5)-1,\quad y=-3/4 (x+5)-1