# Circle and matrices

• Apr 22nd 2010, 09:33 PM
Anemori
Circle and matrices
I have three points to determine a circle by using matrices 3x3 linear and general form. How do you do this?

a) points (2,6), (-5,-1) and (-2,8)

anyone pls help! thanks
• Apr 23rd 2010, 12:29 PM
Opalg
Quote:

Originally Posted by Anemori
I have three points to determine a circle by using matrices 3x3 linear and general form. How do you do this?

a) points (2,6), (-5,-1) and (-2,8)

The equation of a circle has the form $x^2+y^2+2gx+2fy+c=0$. Plugging in the coordinates (2,6), (-5,-1) and (-2,8) for (x,y), you get three equations for g,f and c:

. . . . . \begin{aligned}40+4g+12f+c&=0,\\
26-10g-2f+c&=0,\\
68-2g+16f+c&=0.\end{aligned}

Now write the three equations in matrix form and solve them by the usual reduction process.
• Apr 23rd 2010, 12:48 PM
Anemori
Thanks... i can do those matrices.. if not i'll let you know..