SOLUTION: How were going to transform a general equation of a circle to standard equation

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Question 1006074: How were going to transform a general equation of a circle to standard equation
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the Squares for the variables.

Ax%5E2%2BBx%2BCy%5E2%2BDy%2BE=0 can be general form for a circle. Let this be changed because A and B would be equal if this is a circle.

Instead, say highlight_green%28x%5E2%2BAx%2By%5E2%2BBy%2BC=0%29, now the coefficients no longer being the same values as the previous general form equation. Continue working with this one.


%28x%2B%28A%2F2%29%29%5E2%2B%28y%2BB%2F2%29%5E2=%28A%5E2%2BB%5E2%29%2F4-C
%28x%2BA%2F2%29%5E2%2B%28y%2BB%2F2%29%5E2=%28A%5E2%2BB%5E2%29%2F4-4C%2F4
highlight%28%28x%2BA%2F2%29%5E2%2B%28y%2BB%2F2%29%5E2=%28A%5E2%2BB%5E2-4C%29%2F4%29--------this is the standard form, equivalent to the general form.

You would need to make some adjustments if the coefficients on x^2 and y^2 are not both equal to 1, before you start the conversion for your specific equation.

The center of the circle would be at x=-A%2F2, y=-B%2F2, and the radius is sqrt%28A%5E2%2BB%5E2-4C%29%2F2.