What is x^2-1/2 y^2-1/2 y=0 ?

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

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x^2-1/2 y^2-1/2 y=0

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

y^{2} - 5 x^{2} + 20 x = 50

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 4 ) ^{2}}{40} = 1

4 x^{2} - 9 y^{2} + 24 x + 18 y - 9 = 0

2 x^{2} - 3 y^{2} < 1

x^{2} = \frac{x}{2} + y^{2}

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