What is the asymptotes of 16y^2-x^2+2x+64y-1=0 ?

The asymptotes of 16y^2-x^2+2x+64y-1=0 is y=(x-1)/4-2,\quad y=-(x-1)/4-2

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asymptotes of 16y^2-x^2+2x+64y-1=0

asymptotes

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0

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

Solution steps

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

Calculate Hyperbola properties

16 y^{2} - x^{2} + 2 x + 64 y - 1 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 2), a = 2, b = 8

y = \frac{2}{8} (x - 1) + (- 2), y = - \frac{2}{8} (x - 1) + (- 2)

Refine

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

5 x^{2} - 5 y^{2} + 20 x - 60 y = 185

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{64} = 1

\frac{y ^{2}}{49} - \frac{x ^{2}}{36} = 1

What is the asymptotes of 16y^2-x^2+2x+64y-1=0 ?
The asymptotes of 16y^2-x^2+2x+64y-1=0 is y=(x-1)/4-2,\quad y=-(x-1)/4-2