Hello, thetomps!
i am not sure what formula to use for this question
Formula? . . . Just the general equation of the circle:
. \(\displaystyle (x\,-\,h)^2\,+\,(y\,-\,k)^2\:=\:r^2\)
And we have to "hammer" our equation into that form.
Find the center and radius of the circle given by the equation
\(\displaystyle x^2\,+\,y^2\,+\,10x\,-\,8y\,-\,8\:=\: 0\)
We have:
.\(\displaystyle x^2\,+\,10x\,+\,y^2\,-\,8y\:=\:8\)
Complete the square:
.\(\displaystyle x^2\,+\,10x\)
+ 25 \(\displaystyle +\,y^2\,-\,8y\)
+ 16\(\displaystyle \:=\:8\)
+ 25 + 16
Factor and simplify:
.\(\displaystyle (x\,+\,5)^2\,+\,(y\,-\,4)^2\:=\:49\)
Therefore:
.Center (-5,4), Radius 7