Derive circle equation

What you'll learn

1. Derive the equation of a circle with center (h, k) and radius r using the Pythagorean Theorem and the distance formula
2. Write the equation of a circle in standard form: (x - h)² + (y - k)² = r²
3. Identify the center and radius of a circle given its equation in standard form
4. Complete the square to convert a circle's equation from general form (expanded) to standard form
5. Find the center and radius of a circle given by an equation in general form
6. Explain why the equation (x - h)² + (y - k)² = r² represents all points at distance r from (h, k)

Prerequisites

• Define geometric terms precisely
• Prove theorems using similarity