What is the asymptotes of 16y^2-81x^2-256y+486x=1001 ?

The asymptotes of 16y^2-81x^2-256y+486x=1001 is y= 9/4 (x-3)+8,\quad y=-9/4 (x-3)+8

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asymptotes of 16y^2-81x^2-256y+486x=1001

asymptotes

16 y^{2} - 81 x^{2} - 256 y + 486 x = 1001

y = \frac{9}{4} (x - 3) + 8, y = - \frac{9}{4} (x - 3) + 8

Solution steps

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

Calculate Hyperbola properties

16 y^{2} - 81 x^{2} - 256 y + 486 x = 1001 :

Up-down Hyperbola with

(h, k) = (3, 8), a = 9, b = 4

y = \frac{9}{4} (x - 3) + 8, y = - \frac{9}{4} (x - 3) + 8

4 x^{2} - y^{2} + 40 x - 4 y + 80 = 0

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

- \frac{y ^{2}}{1} + \frac{x ^{2}}{49} = 1

\frac{x ^{2}}{9} - \frac{y ^{2}}{49} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

What is the asymptotes of 16y^2-81x^2-256y+486x=1001 ?
The asymptotes of 16y^2-81x^2-256y+486x=1001 is y= 9/4 (x-3)+8,\quad y=-9/4 (x-3)+8