Solve (D/d)^2=F+P/F-P

$$( \frac { D } { d } ) ^ { 2 } = \frac { F + P } { F - P }$$

Solve for D (complex solution)

$$D=-i\left(F-P\right)^{-\frac{1}{2}}\sqrt{-F-P}d$$

$$D=i\left(F-P\right)^{-\frac{1}{2}}\sqrt{-F-P}d\text{, }d\neq 0\text{ and }F\neq P$$

Solve for F (complex solution)

$$\left\{\begin{matrix}F=\frac{P\left(D^{2}+d^{2}\right)}{D^{2}-d^{2}}\text{, }&d\neq 0\text{ and }P\neq 0\text{ and }D\neq -d\text{ and }D\neq d\\F\neq P\text{, }&\left(D=-d\text{ or }D=d\right)\text{ and }P=0\text{ and }d\neq 0\end{matrix}\right.$$

Solve for D

$$\left\{\begin{matrix}D=0\text{, }&P=-F\text{ and }d\neq 0\text{ and }F\neq 0\\D=\sqrt{\frac{F+P}{F-P}}d\text{; }D=-\sqrt{\frac{F+P}{F-P}}d\text{, }&\left(P\neq 0\text{ and }F=-P\text{ and }d\neq 0\right)\text{ or }\left(d\neq 0\text{ and }F\leq -P\text{ and }F<P\text{ and }|F|\geq |P|\right)\text{ or }\left(d\neq 0\text{ and }F\geq -P\text{ and }F>P\text{ and }|F|\geq |P|\right)\end{matrix}\right.$$

Solve for F

$$\left\{\begin{matrix}F=\frac{P\left(D^{2}+d^{2}\right)}{D^{2}-d^{2}}\text{, }&d\neq 0\text{ and }P\neq 0\text{ and }|D|\neq |d|\\F\neq 0\text{, }&P=0\text{ and }|D|=|d|\text{ and }d\neq 0\end{matrix}\right.$$