Solve y=x^2/2r-1

$$y = \frac { x ^ { 2 } } { 2 r - 1 }$$

Solve for r

$$\left\{\begin{matrix}r=\frac{x^{2}+y}{2y}\text{, }&x\neq 0\text{ and }y\neq 0\\r\neq \frac{1}{2}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable r cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2r-1.

$$y\left(2r-1\right)=x^{2}$$

Use the distributive property to multiply y by 2r-1.

$$2yr-y=x^{2}$$

Add y to both sides.

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

Divide both sides by 2y.

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

Dividing by 2y undoes the multiplication by 2y.

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

Variable r cannot be equal to \frac{1}{2}.

$$r=\frac{x^{2}+y}{2y}\text{, }r\neq \frac{1}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{y\left(2r-1\right)}$$

$$x=\sqrt{y\left(2r-1\right)}\text{, }r\neq \frac{1}{2}$$

Solve for x

$$x=\sqrt{y\left(2r-1\right)}$$

$$x=-\sqrt{y\left(2r-1\right)}\text{, }\left(y\geq 0\text{ and }r>\frac{1}{2}\right)\text{ or }\left(y\leq 0\text{ and }r<\frac{1}{2}\right)$$