SOLUTION: This problem deals with a circle. Enter your answers as alebraic expressions in A, B, and C. Consider the equation {{{x^2+y^2+Ax+By+C=0}}} It describes a circle with cent

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: This problem deals with a circle. Enter your answers as alebraic expressions in A, B, and C. Consider the equation {{{x^2+y^2+Ax+By+C=0}}} It describes a circle with cent      Log On


   

Question 19912: This problem deals with a circle. Enter your answers as alebraic expressions in A, B, and C. Consider the equation

x%5E2%2By%5E2%2BAx%2BBy%2BC=0

It describes a circle with center h,k and a radius r where
h=
k=
r=

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You need to get your equation into the standard form for a circle with center at (h, k) and radius r. %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2You can do this by completing the square in the x-terms and in the y-terms.
x%5E2%2By%5E2%2BAx%2BBy%2BC=0 Group the x-terms and the y-terms.
%28x%5E2%2BAx%29+%2B+%28y%5E2%2BBy%29%2BC=0 Now subtract C from both sides of the equation.
%28x%5E2%2BAx%29+%2B+%28y%5E2%2BBy%29+=+-C Complete the square in the x-terms and in the y-terms.
%28x%5E2%2BAx%2BA%5E2%2F4%29+%2B+%28y%5E2%2BBy%2BB%5E2%2F4%29+=+A%5E2%2F4+%2B+B%5E2%2F4+-+C Factor the x-group and the y-group and simplify.
%28x%2BA%2F2%29%5E2+%2B+%28y%2BB%2F2%29%5E2+=+%28A%5E2%2BB%5E2-4C%29%2F4 Compare this with:
%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2
h+=+-A%2F2
k+=+-B%2F2
r+=+%281%2F2%29sqrt%28A%5E2%2BB%5E2-4C%29