Orthogonal trajectory

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In mathematics, orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles.

For example, each straight line passing through the origin, y = mx is an orthogonal trajectory of the family of the circles x² + y² = r².

The problem is classical, but is now understood by means of complex analysis; see for example harmonic conjugate.

[edit] External links

Exploring orthogonal trajectories - applet allowing user to draw families of curves and their orthogonal trajectories.