Center of a Circle Calculator
Find the center and radius from x²+y²+Dx+Ey+F=0.
Formula
h=−D/2; k=−E/2; r=√(D²/4+E²/4−F).
Center x (coordinate unit) ≈ -(-6)÷2 · Center y (coordinate unit) ≈ -(4)÷2 · Radius (coordinate unit) ≈ sqrt((-6)^2÷4+(4)^2÷4-(-12))+0÷((-6)^2÷4+(4)^2÷4-(-12))
How to use
- Normalize the x² and y² coefficients to 1.
- Enter D, E and F with their signs.
- Read center (h,k) and radius.
Examples
- D=−6, E=4, F=−12 give center (3,−2), radius 5.
Frequently asked questions
Which equations are accepted?
Circles with equal x² and y² coefficients and no xy term, after normalization.
What if r² is zero or negative?
The equation is degenerate or has no real circle; no result is returned.
What units are used?
Coordinates and radius use the same coordinate unit.
Sources
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