MATH CALCULATOR
General Form Equation Circle Calculator
Calculate the radius and center of a circle using its general form equation.
What is the General Form Equation Circle Calculator & How does it work?
The general form equation of a circle is given by:To find the center (h, k) and radius r of the circle, we complete the square for both x and y terms.The center (h, k) is given by:The radius r is calculated as:
Ax^2 + Ay^2 + Dx + Ey + F = 0
A = coefficient of x2 and y2, D = coefficient of x, E = coefficient of y, F = constant term
h = -frac{D}{2A}, quad k = -frac{E}{2A}
r = sqrt{h^2 + k^2 – frac{F}{A}}
Parameters
Result—
Frequently Asked Questions
How do I find the center of a circle from its general form equation?
To find the center (h, k), use the formulas h = -D/(2A) and k = -E/(2A).
What is the formula for the radius of a circle in general form?
The radius r can be calculated using the formula r = sqrt(h^2 + k^2 – F/A), where h and k are the center coordinates.
Can this calculator handle all types of circles?
Yes, as long as the equation is in the general form Ax^2 + Ay^2 + Dx + Ey + F = 0, with A ≠ 0.
What if my circle’s equation doesn’t have an x or y term?
If there’s no x or y term, the coefficient D or E is zero. The center will be at (h, k) where h = -D/(2A) and k = -E/(2A).
How do I convert a standard form circle equation to general form?
To convert from standard form (x-h)^2 + (y-k)^2 = r^2, expand and rearrange terms to match Ax^2 + Ay^2 + Dx + Ey + F = 0.
Is this calculator suitable for circles with non-integer coefficients?
Yes, the calculator can handle equations with any real number coefficients, including decimals and fractions.
What should I do if A is not equal to 1 in my equation?
If A ≠ 1, ensure all terms are divided by A before applying the formulas for h, k, and r.
Results are for informational purposes only and do not constitute professional advice.