# Equation of a circle from three points calculator

To find the equation of a circle passing through three points, follow these steps:

1. Calculate the midpoint of two of the points. Suppose we have three points, A(x1, y1), B(x2, y2), and C(x3, y3), then we can select any two points, say A and B, and calculate their midpoint M((x1+x2)/2, (y1+y2)/2).
2. Calculate the slope of the line passing through points A and B. The slope of the line is given by m = (y2 – y1) / (x2 – x1).
3. Calculate the slope of the line perpendicular to AB. The slope of the line perpendicular to AB is given by -1/m.
4. Calculate the midpoint of the line perpendicular to AB that passes through M. This point is the center of the circle.
5. Calculate the radius of the circle. The radius is given by the distance between the center and any of the three points, such as A, B or C.
6. Write the equation of the circle in standard form. The equation of the circle is (x – h)^2 + (y – k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

You can use the above steps manually or you can use an online calculator to find the equation of a circle from three points.