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Equation of a Circle
Coordinate Geometry • Grades 9, 10, 11
Coordinate Geometry
Equation of a Circle
Write and graph the standard algebraic equation of a circle centered at (h, k) with radius r.
The Formula
(x - h)² + (y - k)² = r²
Used for: Writing and graphing the standard algebraic equation of a circle centered at (h, k) with radius r
(h, k)Center coordinates of the circle
rRadius of the circle
r²Square of radius
⚡Live Interactive Quick Solver
Instant CalculationStandard Circle Equation:(x - 2)² + (y + 1)² = 25
Center: (2, -1) • Radius: 5 • Area: 78.54
(x - h)^2 + (y - k)^2 = r^2
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🎯 Key Concepts & Rules
Essential principles for calculating with this formula:
⭕
(x - h)² + (y - k)² = r²Standard form with center (h, k) and radius r.
📍
Center at Origin (0,0)Simplifies to x² + y² = r².
📝 Worked Examples & Step-by-Step Solutions
Example 1: Center (3, -2), Radius 4
Problem:
Write equation of circle with center (3, -2) and radius 4.1
Identify
h = 3, k = -2, r = 42
Substitute
(x - 3)² + (y - (-2))² = 4²3
Simplify
(x - 3)² + (y + 2)² = 16Answer: (x - 3)² + (y + 2)² = 16
💡 Pro Tips & Common Mistakes
Sign Flip Trap
Notice that (x - 3) means h = +3, and (y + 2) means k = -2.
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