What is the asymptotes of y^2-4x^2<1 ?

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

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asymptotes of y^2-4x^2<1

asymptotes

y^{2} - 4 x^{2} < 1

y = 2 x, y = - 2 x

Solution steps

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

Rewrite as

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

Calculate Hyperbola properties

y^{2} - 4 x^{2} = 1 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 1, b = \frac{1}{2}

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

Refine

y = 2 x, y = - 2 x

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

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{256} = 1

x^{2} - 4 y^{2} - 4 x + 24 y - 36 = 0

\frac{y ^{2}}{4} - \frac{x ^{2}}{36} = 1

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