What is the asymptotes of y^2-4x^2+4x-2y-4=0 ?

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

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asymptotes of y^2-4x^2+4x-2y-4=0

asymptotes

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

y = 2 x, y = - (2 x - 1) + 1

Solution steps

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

Calculate Hyperbola properties

y^{2} - 4 x^{2} + 4 x - 2 y - 4 = 0 :

Up-down Hyperbola with

(h, k) = (\frac{1}{2}, 1), a = 2, b = 1

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

Refine

y = 2 x, y = - (2 x - 1) + 1

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

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

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