What is the asymptotes of-4x^2+y^2-2y=3 ?

The asymptotes of-4x^2+y^2-2y=3 is y=2x+1,\quad y=-2x+1

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asymptotes of-4x^2+y^2-2y=3

asymptotes

- 4 x^{2} + y^{2} - 2 y = 3

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

Solution steps

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

Calculate Hyperbola properties

- 4 x^{2} + y^{2} - 2 y = 3 :

Up-down Hyperbola with

(h, k) = (0, 1), a = 2, b = 1

y = \frac{2}{1} (x - 0) + 1, y = - \frac{2}{1} (x - 0) + 1

Refine

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

5 y^{2} - 2 x^{2} = 9

- x^{2} + y^{2} = 1

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

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

x^{2} - 9 y^{2} = 144

What is the asymptotes of-4x^2+y^2-2y=3 ?
The asymptotes of-4x^2+y^2-2y=3 is y=2x+1,\quad y=-2x+1