Write the general equation for the circle that passes through the points: (0,0) (6,0) (0,-8)

Step-by-step explanation:

We start by writing the general form of the equation of a circle of radius R centered at and creating three equations (one for each unknown: , , and the radius R):

1) If the circle passes through (0,0) then we should have that the equation above holds true:

2) If the circle passes through (6,0) then we should have that the equation above holds true, and we also can use the important result from part 1) () to solve for :

3) If the circle passes through (0,-8) then we should have that the general equation of the circle above holds true, and we also can use the important result from part 1) () to solve for :

4) and finally, we use the results for and of parts 2) and 3) back into the equation in part 1) to solve for :

Then, replacing , , and for the values we found, the equation of the circle becomes:

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step-by-step explanation: