What is the asymptotes of 2x^2-3y^2=6 ?

The asymptotes of 2x^2-3y^2=6 is y=sqrt(2/3)x,\quad y=-sqrt(2/3)x

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asymptotes of 2x^2-3y^2=6

asymptotes

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

y = \frac{2}{3} x, y = - \frac{2}{3} x

Solution steps

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

Calculate Hyperbola properties

2 x^{2} - 3 y^{2} = 6 :

Right-left Hyperbola with

(h, k) = (0, 0), a = 3, b = 2

y = \frac{2}{3} (x - 0) + 0, y = - \frac{2}{3} (x - 0) + 0

Refine

y = \frac{2}{3} x, y = - \frac{2}{3} x

6 x^{2} - 36 y^{2} = 2304

9 y^{2} - 16 x^{2} - 256 = 0

- 9 x^{2} + y^{2} = 36

y^{2} = x^{2} - 1

\frac{( y + 2 ) ^{2}}{36} - x^{2} = 1

What is the asymptotes of 2x^2-3y^2=6 ?
The asymptotes of 2x^2-3y^2=6 is y=sqrt(2/3)x,\quad y=-sqrt(2/3)x