Introduction to Conic Sections: The Circle

This document provides a comprehensive overview of the Circle as a conic section within a Pre-Calculus context. It begins by defining the geometric properties of a circle—specifically the center, radius, and diameter—and explains how the distance formula (derived from the Pythagorean Theorem) leads to the Standard Equation of a Circle. The notes further detail the transition from standard form to General Form through algebraic expansion. The page concludes with three practical examples: 1. Writing an equation for a circle centered at the origin (0,0). 2. Writing an equation for a circle with a shifted center (h, k). 3. Calculating the center and radius using the midpoint and distance formulas when only the endpoints of a diameter are provided.