What is 3x^2-3y^2=2y ?

The solution to 3x^2-3y^2=2y is Hyperbola with (h,k)=(0,-1/3),a= 1/3 ,b= 1/3

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3x^2-3y^2=2y

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

(h, k) = (0, - \frac{1}{3}), a = \frac{1}{3}, b = \frac{1}{3}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{1}{3}), a = \frac{1}{3}, b = \frac{1}{3}

16 x^{2} - 9 y^{2} - 90 y - 369 = 0

y^{2} - z^{2} + 2 z - 4 = 0

9 x^{2} - 4 y^{2} - 54 x + 8 y - 113 = 0

\frac{( y + 2 ) ^{2}}{25} - \frac{( x - 6 ) ^{2}}{9} = 1

5 y^{2} + 30 y + 8 x - 79 - 4 x^{2} = 0

What is 3x^2-3y^2=2y ?
The solution to 3x^2-3y^2=2y is Hyperbola with (h,k)=(0,-1/3),a= 1/3 ,b= 1/3