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.

Construct the ellipse as an envelope of its tangents.
Fix a point P inside a circle C. Show that the line perpendicular to the
line segment joining P and a variable point Q on C envelopes an ellipse.
Given a point outside an ellipse,
construct the pair of tangents to the ellipse passing through the point.
Given a point and a circle, find the locus of the circle passing through
the point and tangent to the circle. There are four cases to consider:
Given two circles, find the locus of the center of the common tangent
circle.
There are several cases to consider: