Solve y=x^2/2p

$$y = \frac { x ^ { 2 } } { 2 p }$$

Solve for p

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

Steps for Solving Linear Equation

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2p.

$$y\times 2p=x^{2}$$

Reorder the terms.

$$2py=x^{2}$$

The equation is in standard form.

$$2yp=x^{2}$$

Divide both sides by 2y.

$$\frac{2yp}{2y}=\frac{x^{2}}{2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$p=\frac{x^{2}}{2y}$$

Variable p cannot be equal to 0.

$$p=\frac{x^{2}}{2y}\text{, }p\neq 0$$

Solve for x (complex solution)

$$x=-\sqrt{y}\sqrt{2p}$$

$$x=\sqrt{y}\sqrt{2p}\text{, }p\neq 0$$

Solve for x

$$x=\sqrt{2py}$$

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