# The Physics, Astronomy and Mathematics of the Solar System

## Discovering Conic Sections in the Motion of Heavenly Bodies

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## The Parabola

The general equation of the parabola is given as: y-k=a(x-h)^2

In some sense the algebra for the parabola will perhaps be the most familiar to the students. However, they will not probably be familiar with the following definition. A parabola is the set of all points in a plane that are the same distance from a given point (focus) as they are from a given line (directrix). y-k=a(x-h)^2. This is pictured in Figure 4 where any point P will be equidistant from the focus F and the closest point Q on the directrix.

(image available in print form)

Figure 4.
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source:
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Wikipedia

The parabola may be illustrated with the trajectory of a rocket or projectile. A demonstration using a water hose would be useful in showing the shape of the parabola.

Students should be able to write and graph equations of parabolas given their identifying characteristics and identify properties of parabolas from their equations.