Analytic Geometry (in a plane)

• Lines
• Circle
• Parabola
• Ellipse
• Hyperbola
• Homogeneous coordinates and points at infinity
• Transformation of coordinates (Projective; Affine; Metric)
• Imaginary points and lines
• Cross ratios and harmonic conjugate elements
• General equation of a conic section - properties
• Degenerated conic sections and classification
• Reduction of the general equation of a conic section and classification
• Tangent lines
• Asymptotes of a conic section
• Systems of conic sections
• Pole and polar line
• Center-point of a conic section
• Center-line of a conic section
• Axes of an affine conic section
• Foci of a conic section
• Locus of a variable point