What is the asymptotes of 6x^2-2/3 y^2=4 ?

The asymptotes of 6x^2-2/3 y^2=4 is y=3x,\quad y=-3x

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asymptotes of 6x^2-2/3 y^2=4

asymptotes

6 x^{2} - \frac{2}{3} y^{2} = 4

y = 3 x, y = - 3 x

Solution steps

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

Calculate Hyperbola properties

6 x^{2} - \frac{2}{3} y^{2} = 4 :

Right-left Hyperbola with

(h, k) = (0, 0), a = \frac{2}{3}, b = 6

y = \frac{6}{\frac{2}{3}} (x - 0) + 0, y = - \frac{6}{\frac{2}{3}} (x - 0) + 0

Refine

y = 3 x, y = - 3 x

4 (x - 3)^{2} - 9 (y - 2)^{2} = 36

\frac{x ^{2}}{4} - \frac{y ^{2}}{16} = 1

\frac{( x + 1 ) ^{2}}{3} - \frac{( y - 1 ) ^{2}}{5} = 1

9 x^{2} - 4 y^{2} + 72 x + 180 = 0

8 y^{2} - 32 x^{2} = 96

What is the asymptotes of 6x^2-2/3 y^2=4 ?
The asymptotes of 6x^2-2/3 y^2=4 is y=3x,\quad y=-3x