What is x^2= x/2+y^2 ?

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

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x^2= x/2+y^2

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

(h, k) = (\frac{1}{4}, 0), a = \frac{1}{4}, b = \frac{1}{4}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{1}{4} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{1}{4} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{4}, 0), a = \frac{1}{4}, b = \frac{1}{4}

\frac{( x - 2 ) ^{2}}{4} - \frac{( y + 3 ) ^{2}}{1} = 1

\frac{( x - 0 ) ^{2}}{3 ^{2}} - \frac{( y - 0 ) ^{2}}{4 ^{2}} = 1

x^{2} - 4 y^{2} + 2 x + 16 y - 11 = 0

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

9 x^{2} - 4 y^{2} + 36 x - 16 y - 16 = 0

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