What is the asymptotes of 4y^2-2x^2-4y-8x-15=0 ?

The asymptotes of 4y^2-2x^2-4y-8x-15=0 is y=(x+2)/(sqrt(2))+1/2 ,\quad y=-(x+2)/(sqrt(2))+1/2

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asymptotes of 4y^2-2x^2-4y-8x-15=0

asymptotes

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

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - 2 x^{2} - 4 y - 8 x - 15 = 0 :

Up-down Hyperbola with

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

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

Refine

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

What is the asymptotes of 4y^2-2x^2-4y-8x-15=0 ?
The asymptotes of 4y^2-2x^2-4y-8x-15=0 is y=(x+2)/(sqrt(2))+1/2 ,\quad y=-(x+2)/(sqrt(2))+1/2