SUMMARY
The equation of a circle tangent to the x-axis with a center at (3, 5) is derived using the standard circle equation (x - h)² + (y - k)² = r². Here, h = 3, k = 5, and the radius r is equal to 5, as the circle is tangent to the x-axis. Therefore, the final equation is (x - 3)² + (y - 5)² = 25. This confirms the correct formulation of the circle's equation.
PREREQUISITES
- Understanding of the standard equation of a circle
- Knowledge of Cartesian coordinates
- Familiarity with the concept of tangency in geometry
- Basic algebra skills for manipulating equations
NEXT STEPS
- Study the properties of circles in coordinate geometry
- Learn about the derivation of the equations of conic sections
- Explore the concept of tangents and normals in geometry
- Investigate applications of circles in real-world scenarios
USEFUL FOR
Students studying geometry, mathematics educators, and anyone interested in understanding the properties and equations of circles.