Circle Center
Find the center and radius of a circle from its quadratic equation Ax^2+Ay^2+Bx+D=0 with this free online circle center calculator. Get instant center coordinates (h,k) and radius.
About This Calculator
This circle center calculator finds the center coordinates (h, k) and radius of a circle given its quadratic equation in the standard form A(x^2 + y^2) + Bx + D = 0. Simply enter the coefficients A, B, and the constant term D to instantly compute the circle's center and radius.
The center is found using the formula h = -B/(2A) and k = 0 (the calculator works for equations without a y term). The radius is derived from r^2 = h^2 - D/A. Ideal for students studying conic sections, analytic geometry, or anyone needing quick and accurate circle property calculations.
Frequently Asked Questions
What equation form does this calculator use?
The calculator uses the form A(x^2 + y^2) + Bx + D = 0, where A is the coefficient of x^2 and y^2, B is the coefficient of x, and D is the constant term. Enter these three values to find the center coordinates (h, k) and radius.
How do you find the center of a circle from an equation?
For a circle in the form A(x^2 + y^2) + Bx + D = 0, the center (h, k) is at (-B/2A, 0) and the radius is the square root of (h^2 - D/A). If the value under the square root is negative, the equation does not represent a real circle.
What if my circle equation has a y term?
This calculator is designed for equations without a y term. If your circle equation includes a y term in the form A(x^2 + y^2) + Bx + Cy + D = 0, you need a calculator that accepts four coefficients instead of three.
Can the coefficient of x^2 + y^2 be zero?
No. The coefficient of x^2 + y^2 (A) must be non-zero for the equation to represent a circle. If A is zero, the equation is no longer quadratic and cannot represent a circle.
Is this tool free?
Yes, all calculators on Calculy are completely free to use with no registration or hidden fees.