SOLUTION: Find the center and radius of the circle whose graph passes through the points (-3,-5), (-9,-13), and (-2,-12). Hint: use the equation x^2+y^2+ax+by+c=0. I need help, I have vari

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Find the center and radius of the circle whose graph passes through the points (-3,-5), (-9,-13), and (-2,-12). Hint: use the equation x^2+y^2+ax+by+c=0. I need help, I have vari      Log On


   

Question 1080854: Find the center and radius of the circle whose graph passes through the points (-3,-5), (-9,-13), and (-2,-12). Hint: use the equation x^2+y^2+ax+by+c=0.
I need help, I have various examples but they skip steps so I don't understand how to solve it.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You will make a system of equations with the form of each equation as ax%2Bby%2Bc=-%28x%5E2%2By%5E2%29, because the right-side member will be a computable value for each equation.

Each point gives a separate equation.



system%28-3a-5b%2Bc=-34%2C-9a-13b%2Bc=-250%2C-2a-12b%2Bc=-148%29------continue and solve this system for a, b, and c.

system%28a=12%2Cb=18%2Cc=92%29
(used online calculator at https://matrix.reshish.com/gauss-jordanElimination.php )

Use the equation formed using the found coefficients and convert the equation into standard equation form for a circle ( can mean, completing the squares) and read the center and radius from the equation.