Question

A circle has the equation x^2+y^2+x-6y+9=0. Find the center and any x or y intercepts.

I know it's a complete the square problem, but I'm messing up somewhere :/

Answer 1

We know:
\[
x^2+y^2+x-6y+9=0
\]So, we complete the square as such:
\[
x^2+y^2+x-6y+9=x^2+x+y^2-6y+9=\\
\left(x+\frac{1}{2}\right)^2+(y-3)^2=\left(\frac{1}{2}\right)^2=\frac{1}{4}
\]

Answer 2

I think you should be able to work from there.

Answer 3

Okay that's actually close to what I had, let's work backwards to see where I messed up. Thanks again! Hahah you've helped me multiple times on this, sorry I'm slow :)

Answer 4

Sure thing

Answer 5

Got it!

Answer 6

Nice