Equation of a circle passing through 3 given points

Equation of a circle passing through 3 given points

First point

x

y

Second point

x

y

Third point

x

y

Calculation precision

Digits after the decimal point: 2

Calculate

Center

x

 

y

 

Radius

 

Equation of a circle in standard form

 

Equation of a circle in general form

 

Parametric equations of a circle

 

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How to find a circle passing through 3 given points

Let's recall how the equation of a circle looks like in general form:

Since all three points should belong to one circle, we can write a system of equations.

The values , and are known. Let's rearrange with respect to unknowns a, b and c.

Now we have three linear equations for three unknowns - system of linear equations with the following matrix form:

We can solve it using, for example, Gaussian elimination like in Gaussian elimination. No solution means that points are co-linear, and it is impossible to draw a circle through them.
The coordinates of a center of a circle and it's radius related to the solution like this

Knowing center and radius, we can get the equations using Equation of a circle calculator