Circle Properties from Equation
How It Works
This circle properties from equation uses established formulas to provide accurate results.
The basic rule:
- h = -D/2, k = -E/2
- r = √((D/2)² + (E/2)² - F)
- (x-h)² + (y-k)² = r²
- Area = πr², Circumference = 2πr
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
How do I find the center and radius from x² + y² + Dx + Ey + F = 0?
The center is (-D/2, -E/2) and the radius is √((D/2)² + (E/2)² - F). This comes from completing the square on both x and y terms.
What does completing the square mean for circles?
Completing the square converts the general form x² + y² + Dx + Ey + F = 0 into standard form (x-h)² + (y-k)² = r² by adding the right constants to both sides.
When does the equation not represent a circle?
If (D/2)² + (E/2)² - F ≤ 0, the equation does not represent a real circle. If it equals 0, you get a single point (degenerate circle). If negative, there are no real solutions.
What if the coefficients of x² and y² are not 1?
First divide the entire equation by the common coefficient so x² and y² each have coefficient 1. For example, 2x² + 2y² + 4x - 6y + 1 = 0 becomes x² + y² + 2x - 3y + 0.5 = 0.