OsculatingCircle Command

OsculatingCircle[ <Point>, <Function> ]: Yields the osculating circle of the function in the given point.; Example: OsculatingCircle[(0, 0), x^2] yields x² + y² - y = 0.

OsculatingCircle[ <Point>, <Curve> ]: Yields the osculating circle of the curve in the given point.; Example: OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]] yields x² + y² + 6x = 7.

Following text is about a feature that is supported only in GeoGebra 5.0.

Note: From GeoGebra 5, this command will work with conics as well.

OsculatingCircle[ <Point>, <Object> ]

Yields the osculating circle of the object (function, curve, conic) in the given point.

Examples:

OsculatingCircle[(0, 0), x^2] yields x² + y² - y = 0
OsculatingCircle[(1, 0), Curve[cos(t), sin(2t), t, 0, 2π]] yields x² + y² + 6x = 7
OsculatingCircle[(-1, 0), Conic[{1, 1, 1, 2, 2, 3}]] yields x² + y² + 2x + 1y = -1