Determine the center and radius of the circle x^2 + y^2 - 10x + 8y - 8 = 0.
So first we can start by adding 8 to both sides of the equation.
\(x^2 + y^2 - 10x + 8y = 8\)
Let's start by completing the square for \(x^2-10x\)
\((x-5)^2\). But, we have an extra \(+25\) term, so we have to subtract 25.
If we complete the square for \(y^2+8y\), we get \((y+4)^2\). But, we have an extra \(+16\) term, so we have to subtract 16.
So, our equation now looks like
I'm assuming you know the form of the circle, so you should be able to do the rest from here easily. You got this! :)
I hope this helped you, guest!