Question 1006074
Complete the Squares for the variables.


{{{Ax^2+Bx+Cy^2+Dy+E=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(x^2+Ax+y^2+By+C=0)}}}, now the coefficients no longer being the same values as the previous general form equation.  Continue working with this one.


{{{x^2+Ax+(A/2)^2+y^2+By+(B/2)^2=-C+(A/2)^2+(B/2)^2}}}
{{{(x+(A/2))^2+(y+B/2)^2=(A^2+B^2)/4-C}}}
{{{(x+A/2)^2+(y+B/2)^2=(A^2+B^2)/4-4C/4}}}
{{{highlight((x+A/2)^2+(y+B/2)^2=(A^2+B^2-4C)/4)}}}--------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/2}}}, {{{y=-B/2}}}, and the radius is  {{{sqrt(A^2+B^2-4C)/2}}}.