## Parabolas

One of the basic problems in algebra is to determine rational solutions or points (where both x and y are rational numbers) to polynomial equations in two or more variables. Conic sections provide basic examples for which it is easy to determine rational points that lie of on these curves. This point alone in conjunction with the effort we made in the early modules on finding rational solutions to polynomial equations in single variable ought to provide sufficient motivation to study conic sections. They are useful in the study of Kepler's laws of planetary motion, in the design of satellite dishes, in analytic geometry and the study of Diophantine equations.

**Review: **Definition and standar equatoin of a circle, distance formula

**Learning Objectives: **In this module, we will study **Parabolas**

- Definition of a parabola
- Directrix and focus
- Standard equation of a vertical and a horizontal parabola
- Vertex
- Eccentricity
- Graph