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

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

asymptotes

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

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 :

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

4 x^{2} - 9 y^{2} - 36 < 0

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

9 y^{2} - 16 x^{2} = 144

(x - 5)^{2} - (y - 4)^{2} = 1

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