The equation of the circle can be written in general form as ...
... x² +y² +ax +by +c = 0
Substituting the given points, this equation becomes
... (-1)² +3.2² + (-1)a +3.2b +c = 0
... (-8)² +4² + (-8)a +4b +c = 0
... (-6.5)² +(-9.3)² + (-6.5)a +(-9.3)b +c = 0
In augmented matrix form, the system of equations is
[tex] \left[\begin{array}{ccc|c}-1&3.2&1&-11.24\\-8&4&1&-80\\-6.5&-9.3&1&-128.74\end{array}\right] [/tex]
The solution to this set of equations can be found using the matrix solver on your calculator. It is ...
[tex]a\approx 10.3754080522\\b\approx 4.83482045702\\c\approx -16.3360174102[/tex]
So, the equation for the circle in general form is
... x² + y² + 10.3754x + 4.8348y - 16.336 = 0