circle

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!

:)