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

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

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y^2-y-x^2=0

y^{2} - y - x^{2} = 0

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

Solution steps

y^{2} - y - x^{2} = 0

Rewrite

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

Therefore Hyperbola properties are:

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

\frac{( x - 7 ) ^{2}}{64} - \frac{( y - 6 ) ^{2}}{36} = 1

\frac{y ^{2}}{144} - \frac{x ^{2}}{25} = 1

25 y^{2} - x^{2} = 100

p^{2} + p = q^{2}

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

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