How to Calculate Circle Equation
What is Circle Equation?
The standard form of a circle equation is (x − h)² + (y − k)² = r², where (h, k) is the centre and r is the radius. This form makes it easy to identify the centre and radius directly.
Formula
(x − h)² + (y − k)² = r²
- h
- x-coordinate of center
- k
- y-coordinate of center
- r
- radius (length)
- x
- x-coordinate on circle
- y
- y-coordinate on circle
Step-by-Step Guide
- 1Standard form: (x − h)² + (y − k)² = r²
- 2Centre is at (h, k)
- 3Radius r = √[(x−h)² + (y−k)²]
- 4Area = πr², Circumference = 2πr
Worked Examples
Input
Centre (2, 3), r = 5
Result
(x − 2)² + (y − 3)² = 25
Input
Centre (0, 0), r = 7
Result
x² + y² = 49
Frequently Asked Questions
What is the general form of a circle equation?
The general form is x² + y² + Dx + Ey + F = 0. You can convert to standard form by completing the square.
Can a circle have a center not at the origin?
Yes! Any point (h, k) can be the center. The standard form directly shows the center and radius.
How do I find the center and radius from the general form?
Complete the square: h = −D/2, k = −E/2, and r² = h² + k² − F.
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