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

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

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}

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

9 x^{2} - 16 y^{2} - 54 x + 64 y - 127 = 0

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

- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0

\frac{y ^{2}}{16} - \frac{x ^{2}}{36} = 1

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