Solve y=k1/x^2

$$y = k \frac { 1 } { x ^ { 2 } }$$

Solve for k

$$k=yx^{2}$$

$$x\neq 0$$

Solution Steps

Multiply both sides of the equation by x^{2}.

$$yx^{2}=k\times 1$$

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

$$k\times 1=yx^{2}$$

Reorder the terms.

$$k=yx^{2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-y^{-\frac{1}{2}}\sqrt{k}\text{; }x=y^{-\frac{1}{2}}\sqrt{k}\text{, }&k\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&y=0\text{ and }k=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{k}{y}}\text{; }x=-\sqrt{\frac{k}{y}}\text{, }&\left(y<0\text{ and }k<0\right)\text{ or }\left(y>0\text{ and }k>0\right)\\x\neq 0\text{, }&y=0\text{ and }k=0\end{matrix}\right.$$