What is the asymptotes of 4x^2-1/2 y^2+8x+2y-2=0 ?

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

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asymptotes of 4x^2-1/2 y^2+8x+2y-2=0

asymptotes

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0

y = 22 (x + 1) + 2, y = - 22 (x + 1) + 2

Solution steps

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

Calculate Hyperbola properties

4 x^{2} - \frac{1}{2} y^{2} + 8 x + 2 y - 2 = 0 :

Right-left Hyperbola with

(h, k) = (- 1, 2), a = 1, b = 22

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

Refine

y = 22 (x + 1) + 2, y = - 22 (x + 1) + 2

\frac{x ^{2}}{10} - \frac{y ^{2}}{90} = 1

\frac{y ^{2} - x ^{2}}{9} = 1

x^{2} - 3 y^{2} - 2 x - 6 y + 7 = 0

16 x^{2} - 9 y^{2} - 96 x + 288 = 0

10 x^{2} - 25 y^{2} = 100

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