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 Nicolaus II Bernoulli in 1720 as a challenge to the English Newtonian school of mathematics.