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

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

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x^2-2y=3y^2

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

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

Solution steps

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

Rewrite

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

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}

4 x^{2} - y^{2} = 36

4 x^{2} - 3 y^{2} - 5 x + 2 y + 1 = 0

(\frac{x ^{2}}{a ^{2}}) - (\frac{y ^{2}}{b ^{2}}) = 1

y^{2} - 4 x^{2} = 1

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

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