What is the asymptotes of 4y^2-x^2=900 ?

The asymptotes of 4y^2-x^2=900 is y= x/2 ,\quad y=-x/2

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asymptotes of 4y^2-x^2=900

asymptotes

4 y^{2} - x^{2} = 900

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

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - x^{2} = 900 :

Up-down Hyperbola with

(h, k) = (0, 0), a = 15, b = 30

y = \frac{15}{30} (x - 0) + 0, y = - \frac{15}{30} (x - 0) + 0

Refine

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

9 (x - 1)^{2} - 16 (y + 2)^{2} = 144

9 x^{2} - y^{2} + 6 y - 18 = 0

4 x^{2} - y^{2} - 24 x - 6 y + 23 = 0

y^{2} - x^{2} = \frac{4}{25}

3 x^{2} - y^{2} + 6 x - 2 y = 10

What is the asymptotes of 4y^2-x^2=900 ?
The asymptotes of 4y^2-x^2=900 is y= x/2 ,\quad y=-x/2