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

The solution to 6x^2-2/3 y^2=4 is Hyperbola with (h,k)=(0,0),a=sqrt(2/3),b=sqrt(6)

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

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

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

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

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

(x - 3)^{2} = 8 + (y + 5)^{2}

\frac{( x + 3 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

What is 6x^2-2/3 y^2=4 ?
The solution to 6x^2-2/3 y^2=4 is Hyperbola with (h,k)=(0,0),a=sqrt(2/3),b=sqrt(6)