What is the asymptotes of 16y^2-x^2+2x+64y+47=0 ?

The asymptotes of 16y^2-x^2+2x+64y+47=0 is y= 1/4 (x-1)-2,\quad y=-1/4 (x-1)-2

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asymptotes of 16y^2-x^2+2x+64y+47=0

asymptotes

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0

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

Solution steps

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

Calculate Hyperbola properties

16 y^{2} - x^{2} + 2 x + 64 y + 47 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 2), a = 1, b = 4

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

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

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

y^{2} - 4 x^{2} - 12 y - 16 x + 16 = 0

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

+ \frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1

What is the asymptotes of 16y^2-x^2+2x+64y+47=0 ?
The asymptotes of 16y^2-x^2+2x+64y+47=0 is y= 1/4 (x-1)-2,\quad y=-1/4 (x-1)-2