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
The equation of a circle has the form $\displaystyle x^2+y^2+2gx+2fy+c=0$. Plugging in the coordinates (2,6), (-5,-1) and (-2,8) for (x,y), you get three equations for g,f and c:
. . . . .$\displaystyle \begin{aligned}40+4g+12f+c&=0,\\
26-10g-2f+c&=0,\\
68-2g+16f+c&=0.\end{aligned}$
Now write the three equations in matrix form and solve them by the usual reduction process.