What is (y+1)^2=x^2-x ?

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

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(y+1)^2=x^2-x

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x, x^{2} + 6 x + 34 = h (x)^{2}

\frac{x ^{2}}{4} - \frac{y ^{2}}{49} = 1

9 x^{2} - 4 y^{2} + 54 x + 16 y + 66 = 0

x^{2} = (13 y^{2} + 1)

a^{2} - b^{2} = 424

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