OsculatingCircle Command

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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
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