Function Repository Resource:

# Orthotomic (1.0.0)current version: 1.0.1 »

Compute the orthotomic of a curve

Contributed by: Eric W. Weisstein  |  Enrique Zeleny
 ResourceFunction["Orthotomic"][c,t] computes the orthotomic in parameter t of a curve c with respect to the point {0,0}. ResourceFunction["Orthotomic"][c,p,t] computes the orthotomic with respect to the point p.

## Details and Options

The orthotomic curve (also known as secondary caustic) is the reflection of the rays of a source in the tangents of points of a curve.
The orthotomic of a curve is the homothetic image (magnified by a factor of 2 with respect to the center of similarity p) of the pedal.

## Examples

### Basic Examples (2)

Orthotomic of a circle with respect to the point {1,1}:

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Orthotomic of a figure eight:

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### Properties and Relations (1)

Pedal curves look similar to the orthotomic:

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## Version History

• 1.0.1 – 29 March 2022
• 1.0.0 – 15 April 2020