
Re: Three Points and a Circle
Posted:
Aug 2, 1993 11:14 AM


The question is how to calculate the Cartesian equation of a circle given the coordinates of three of its points.
Let the points be (x1,y1), (x2,y2), and (x3,y3). Then the circle is given by
/ \  1 x y x^2 + y^2  det  1 x1 y1 x1^2 + y1^2  = 0  1 x2 y2 x2^2 + y2^2   1 x3 y3 x3^2 + y3^2  \ /
This equation is clearly a circle from its form, and it passes through each of the three points because when (x,y) equals one of those points, two rows of the determinant will be the same.
Similar techniques can be used for many other figures.
Regards, Bret troly@math.ucla.edu

