Hi guest!
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
\((x-5)^2+(y+4)^2-16-25=8\)
\(\boxed{(x-5)^2+(y+4)^2=49}\)
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!
:)