x^2+x=y^2

Solution

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( x ^{(2)} )}{( 9 )} - \frac{( y ^{(2)} )}{( 16 )} = 1

y^{2} - 4 z^{2} = 4

- \frac{y ^{2}}{4} + \frac{z ^{2}}{4} = 1

\frac{( y + 2 ) ^{2}}{4} - \frac{( x - 1 ) ^{2}}{64} = 1

(y - 1)^{2} - 9 (x - 2)^{2} = 9

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