Definition:Orthogonal Trajectories

Definition
Let $f \left({x, y, c}\right)$ define a one-parameter family of curves $F$.

Let $g \left({x, y, c}\right)$ also define a one-parameter family of curves $G$, with the property that:


 * Every curve in $F$ is orthogonal to every curve in $G$.

Then $F$ is a family of (reciprocal) orthogonal trajectories of $G$, and contrariwise.

Historical Note
The problem of orthogonal trajectories was posed by in 1720 as a challenge to the English  school of mathematics.