Given three points, (-1,3.2), (-8,4), and (-6.5,-9.3), determine the equation of the circle that passes through the points. solve the problem by deriving a system of three linear equations (substi- tute the points in the equation) and solve the system.

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

The solution to this set of equations can be found using the matrix solver on your calculator. It is ...

So, the equation for the circle in general form is

... x² + y² + 10.3754x + 4.8348y - 16.336 = 0

step-by-step explanation:

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