SUMMARY
The equation of the circle tangent to the x-axis with center at (3,5) is derived using the formula for a circle. The radius is determined to be 5, as it is the vertical distance from the center (3,5) to the x-axis (y=0). Substituting the center coordinates and radius into the standard circle equation results in (x - 3)² + (y - 5)² = 25. This confirms that the circle touches the x-axis at the point (3,0).
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 relationship between a circle and its tangent lines
- Explore the derivation of circle equations from geometric principles
- Investigate applications of circles in real-world scenarios
USEFUL FOR
Students studying geometry, mathematics educators, and anyone interested in understanding the properties of circles and their equations.