Welcome to the general form of the equation of a circle calculator, which can help you convert your circle equation from the general form to the standard and parametric forms, or the other way. Here, we'll learn:

  • What the equation of a circle in general form looks like;
  • How to write the equation of a circle in general form; and
  • How to convert the general form of the circle equation to other forms.

What is the equation of a circle in general form?

The general form of the equation of a circle is given as x² + y² + Dx + Ey + F = 0, with the parameters D, E, and F determining the circle's properties such as radius and center.

How do I convert the general equation of a circle to the standard form?

The standard form of the equation of a circle is (x−A)² + (y−B)² = C. We can write the general form of the circle equation to the standard form by calculating the unknowns A, B, and C from the general equation's parameters D, E, and F.

Luckily, that math is easy!

  1. A = −D/2;
  2. B = −E/2; and
  3. C = A² + B² − F.

How do I convert the general equation of a circle to the parametric form?

The parametric form of the equation of a circle is x = A + r cos(α) and y = B + r sin(α). To write the general form of the circle equation to the parametric equation, we calculate the unknowns A, B, and r:

  1. A = −D/2;
  2. B = −E/2; and
  3. r = √(A² + B² − F).

How do I use the general form of the equation of a circle calculator?

The general form of the equation of a circle calculator is easy to use! Here's how:

  1. Enter your circle's equation in the general form at the top of the calculator.
  2. Find your circle rewritten in standard and parametric forms below.
  3. Also find your circle's properties like center, radius, and area at the very bottom.

In the unlikely event that the general form of the equation of a circle calculator doesn't meet your needs, consider one of our other circle calculators:

FAQ

What is the general form of the equation (x−3)² + (y+2)² = 25?

The general form is x² + y² − 6x + 4y − 12 = 0. Converting from the standard form of (x − A)² + (y − B)² = C (with parameters A = 3, B = −2, and C = 25) to x² + y² + Dx + Ey + F = 0, we calculate:

  1. D = −2A = −6;
  2. E = −2B = 4; and
  3. F = A² + B² − C = −12.

What is the general equation of a circle with (x−6)² + (y−6)² = 49?

This circle's general form is x² + y² − 12x − 12y + 23 = 0. We have A = 6, B = 6, and C = 49 in the standard form (x−A)² + (y−B)² = C. So, to convert to x² + y² + Dx + Ey + F = 0, we calculate:

  1. D = −2A = −12;
  2. E = −2B = −12; and
  3. F = A² + B² − C = 23.

What is the general form of the equation of a circle with (x+3)² + (y−5)² = 49?

The general form is x² + y² + 6x − 10y − 15 = 0. Converting from the standard form of (x−A)² + (y−B)² = C (with parameters A = −3, B = 5, and C = 49) to x² + y² + Dx + Ey + F = 0, we calculate:

  1. D = −2A = 6;
  2. E = −2B = −10; and
  3. F = A² + B² − C = −15.
Rijk de Wet
Enter the general equation of your circle below, and we'll show you the standard and parametric equivalents and the circle's center and its properties below.
General equation: x² + y² + Dx + Ey + F = 0
D
E
F
Standard equation: (x − A)² + (y − B)² = C
A
B
C
Parametric equation: x = A + r cos(α), y = B + r sin(α)
A
B
r
Center coordinates
x-coordinate
y-coordinate
Circle properties
Radius
Diameter
Area
Circumference
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