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 what is a conic section conceptually
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Conic Sections are figures that can be formed by slicing a three dimensional right circular cone with a plane. There are different ways to do this, and each way yields a different figure. These figures can be represented on the graph as well as algebraically. The four conic sections are circles, ellipses, parabolas, and hyperbolas.
Conic Sections have been studied for a quite a long time. Kepler first noticed that planets had elliptical orbits. Depending on the energy of an orbiting body, orbit shapes that are any of the four types of conic sections are possible.
A conic section can be formally defined as a set or locus of a point that moves in the plane of a fixed point called the focus and the fixed line is called the directrix.
The general equation for all conics is
and