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Geometric Construction 15

Construct the osculating circle of an ellipse and a hyperbola when
the foci are given.

Construct the osculating circle of a parabola when the focus is given.

Construct the osculating circle of an ellipse which is constructed according
to the parametric equations.

Construct the osculating circle of the hyperbola which is constructed according
to the parametric equations.

Construct a parabola according to this figure:
Form an animation of the osculating circle of the parabola by completing
the above drawing.