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.

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