# Linear Algebra / Gaussian Elimination

1. Jan 17, 2010

### page13

1. The problem statement, all variables and given/known data

Find coefficients a,b,c and d so that the curve of a circle in an xy plane, with points (-4,5), (-2,7) and (4,-3), is given by the equation ax2 + ay2 + bx + cy + d = 0.

Not even sure where to start. Can anyone help me with this?

2. Jan 17, 2010

### Dick

Use Gaussian elimination. Substitute the x and y values for each point into the equation and get three linear equations for a, b, c and d. But you don't have enough equations to get a unique solution. You'll have to express three of those variables in terms of another. You've got to expect this. (ax^2 + ay^2 + bx + cy + d)/k=0 is the same circle for any nonzero k.

3. Jan 17, 2010

### page13

Thanks Dick. I guess I'll get some big ugly fractions in my Row Echelon Form, correct? So far I've got numbers over 53 in the 1st row, over 65 in the 2nd row, and the 3rd row looks like it'll be a 4 digit denominator.

4. Jan 17, 2010

### Dick

Probably. I didn't actually work it out, but it doesn't look like it was set up to come out nice. Sounds like you are the right track though.