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Appendix 5: Conic Sections,
Ellipse, Parabola, and Hyperbola
This appendix has two parts: the algebraic equation of a conic section and polar coordinate repre-
sentation of conic sections. The reader who is not interested in algebraic equations of conic sections
can go directly to the polar coordinate representations of conic sections, which is well suited for
solving orbit problems.
A5.1 ALGEBRAIC EQUATIONS OF CONIC SECTIONS
The circle, ellipse, parabola, and hyperbola are called conic sections because each shape can be
obtained by using a plane to intersect a cone. Any conic section can be represented by a second-
order algebraic equation: ...