plane conics
One of the most beautiful parts of plane geometry is the study of conics.
These were studied by the Greeks. It was Apollonius
who introduced the terms
ellipse, parabola and hyperbola for the three different types.
Plane conics may be defined in three ways:
 as loci satisfying the focusdirectrix property,
 as loci with equations quadratic in x and y,
 as plane sections of a rightcircular cone.
We will see that each approach leads to essentially the same family of curves.
The circle, a special kind of ellipse, does not have a focusdirectrix definition,
but appears naturally in the other approaches.
We shall look at the congruence classes of conics in various geometries. In
particular, we will find that the infinite number of classes in euclidean and in
similarity geometry reduce to just three classes in affine geometry, and to a
single class in projective geometry.
contents

