General form of the equation of a circle

The general form of the equation of a circle is 

`x^2 + y^2 + Cx + Dy + E = 0`

Note that the coefficients of `x^2` and `y^2` will always be the same in the equation of a circle and that in the general form of the equation of a circle, you will never find the `xy` term (that is, the term containing both x and y).

Get center of circle from general form

The coordinates of the center of the circle can be calculated from its equation in the general form by using the completing the square method to convert the equation into standard form. But, the whole procedure is time consuming, and the coordinates of the center of the circle in the general form above are simply `(-C/2, -D/2)`. To know more about how we got that, see this post: "Calculate center coordinates of a circle from its equation in general form"

Get radius of circle from general form

Similarly, the radius of a circle can also be calculated by converting its equation from general to standard form. It comes down to the following formula for the radius:

`r = \sqrt{(C/2)^2 + (D/2)^2 - E}`

To know more about the calculation part (that is, how the above formula was obtained), go see this post: "Calculate radius of a circle from its equation in general form"