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

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

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x^2-y^2+y=0

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

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

Solution steps

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

Rewrite

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

Therefore Hyperbola properties are:

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

x^{2} + (6 - 6) y^{2} = 1

15485863 = 4 x^{2} - y^{2}

(x - y) (x + y) > 4

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

x^{2} - y^{2} - 2 x + 4 y - 12 = 0

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