Geometric Construction 1

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.

1.  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.

1. 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.

1. 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.

1. 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.

1. 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.

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

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

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