SUMMARY
The equation of a circle with center at (-3, 4) and tangent to the y-axis is derived using the radius, which is the distance from the center to the tangent point on the y-axis. The tangent point is identified as (0, 4), leading to a radius of 3. Consequently, the equation of the circle is expressed as (x + 3)² + (y - 4)² = 9, confirming the correct formulation based on the given parameters.
PREREQUISITES
- Understanding of circle equations in coordinate geometry
- Knowledge of the concept of tangents in geometry
- Familiarity with distance formula between two points
- Basic algebra for manipulating equations
NEXT STEPS
- Study the derivation of circle equations from standard forms
- Learn about the properties of tangents to circles
- Explore the distance formula in coordinate geometry
- 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.
