SUMMARY
To find the distance between the centers of two circles, first determine the centers by completing the square for each circle's equation. Once the centers are identified, apply the distance formula: d = √((x2 - x1)² + (y2 - y1)²). This method is confirmed as correct and essential for solving the problem presented.
PREREQUISITES
- Understanding of circle equations and the method of completing the square.
- Familiarity with the distance formula in coordinate geometry.
- Basic algebra skills for manipulating equations.
- Knowledge of Cartesian coordinates.
NEXT STEPS
- Study the process of completing the square for different types of equations.
- Practice using the distance formula with various coordinate pairs.
- Explore applications of distance calculations in geometry and physics.
- Review properties of circles and their equations in analytic geometry.
USEFUL FOR
Students studying geometry, mathematics educators, and anyone needing to understand the relationship between circle equations and distance calculations.