Geometric Construction
1

An ellipse is the locus
of a point which moves so that the sum of its distances from two fixed
points (the loci) is a constant. Construct the ellipse according to this
definition.

A hyperbola is
the locus of a point which moves so that the difference of its distances
from two fixed points (the loci) is a constant. Construct the hyperbola
according to this definition.

A parabola is the locus
of a point which moves so that the sum of its distances a fixed point (the
locus) to a fixed straight line (the directrix) is a constant. Construct
the parabola according to this definition.

Construct an animation displaying
various positions of a pair of orthogonal tangents to an ellipse. Find
the locus of the point of intersection of these two tangents.

Construct an animation displaying
various positions of a pair of orthogonal tangents to a hyperbola. Find
the locus of the point of intersection of these two tangents.

Construct an animation displaying
various positions of a pair of orthogonal tangents to an ellipse. Find
the locus of the point of intersection of these two tangents.

From a given point lying outside
an ellipse, construct the pair of tangents passing through the point.

From a given point lying ``between''
the hyperbola, construct the pair of tangents passing through the point.

From a given point lying ``under''
a parabola, construct the pair of tangents passing through the point.