Function Repository Resource:

OsculatingConic

Get the osculating conic of a plane curve

Contributed by: Jan Mangaldan
 ResourceFunction["OsculatingConic"][c,{t,t0},{x,y}] gives the implicit equation with variables x and y for the osculating conic of a plane curve c depending on parameter t at t=t0.

Details

The osculating conic of a plane curve at a given point is the unique conic that has fourth-order contact with the curve at that point.

Examples

Basic Examples (2)

The implicit Cartesian equation for the osculating conic of a deltoid:

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Plot the deltoid and its osculating conic along with their point of contact:

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Scope (2)

The osculating conic for a catenary:

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Show three of the osculating conics along with the catenary:

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Properties and Relations (1)

Use the resource function ConicProperties to get further information on an osculating conic:

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Version History

• 1.0.0 – 08 March 2021