What is y^2=(4x^2-2)/9 ?

The solution to y^2=(4x^2-2)/9 is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b=(sqrt(2))/3

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y^2=(4x^2-2)/9

y^{2} = \frac{4 x ^{2} - 2}{9}

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{2}{3}

Solution steps

y^{2} = \frac{4 x ^{2} - 2}{9}

Rewrite

y^{2} - \frac{4 x ^{2} - 2}{9} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{2}{3}

X^{2} - Y^{2} - 12 = 0

(x^{2} - y^{2}) = 23

8 y^{2} + 3 y - 9 = 8 x^{2} + 9 x - 3

\frac{y ^{2}}{6} - \frac{x ^{2}}{9} = 1

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

What is y^2=(4x^2-2)/9 ?
The solution to y^2=(4x^2-2)/9 is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b=(sqrt(2))/3