LAC 28:CXLII.2927. Expressing Geometric Properties with Equations

A. Translate between the geometric description and the equation for a conic section. 1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. 2. Derive the equation of a parabola given a focus and directrix. B. Use coordinates to prove simple geometric theorems algebraically. 1. Use coordinates to prove geometric theorems algebraically.