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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