Orthotomic

Given a source $S$ and a curve $\gamma$, pick a point on $\gamma$ and find its tangent $T$. Then the Locus of reflections of $S$ about tangents $T$ is the orthotomic curve (also known as the secondary Caustic). The Involute of the orthotomic is the Caustic. For a parametric curve $(f(t),g(t))$ with respect to the point $(x_0, y_0)$, the orthotomic is

$$x = x_0-{2g'[f'(g-y_0)-g'(f-x_0)]\over f'^2+g'^2}$$

$$y = y_0+{2f'[f'(g-y_0)-g'(f-x_0)]\over f'^2+g'^2}.$$

See also Caustic, Involute

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 60, 1972.