x^2+10x+y^2-10y+46=0
how do you put that in standard form for a circle?
Equation of a circle with centre (a,b) and radius r: $\displaystyle (x-a)^2 + (y-b)^2 = r^2$
Complete the square for x and y:
$\displaystyle (x+5)^2 = x^2+10x {\color{red} +25} \rightarrow x^2+10x = (x+5)^2 {\color{red} -25}$.
You can do the same with y to give $\displaystyle y^2-10y = (y-5)^2 {\color{red} -25}$
Once you've done that collect the constants together and move them over to the right hand side.