Elementary Euclidean Geometry. An Undergraduate Introduction
It is an elementary introduction to the geometry of lines and conics in the Euclidean plane. Classical invariants of the conics and intersection properties of conics and lines are studied there. Also centres, focuses, tangents and normals of conics are discussed and classification of conics is presented. Properties of individual types (parabolas, ellipses, hyperbolas) of conics are described in details. The polarity is defined and used for several constructions. At the end, congruences of conics with respect to motions in the plane are considered and normal forms of conics are introduced. Conics are also studied as conical sections in three dimensional space. There are many examples and exercises.