Solve x^2=2py

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

Solve for p (complex solution)

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

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.

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

Solve for p

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

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.

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

Solve for x (complex solution)

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

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

Solve for x

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

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