Question

x^2+y^2-4x+4y-17=0

find the vertex and radius of the circle

Answer 1

To do this properly you have to rewrite it in the form:

\[(x-h)^2 + (y-k)^2 = r^2\]

Answer 2

group your x terms together
group your y terms together

complete the square for your x's
x^2-4x+(-4/2)^2

complete the square for your y's
y^2+4y+(4/2)^2

see how i took b and divided it by 2 and then squared
find c so that it completes the square
g^2+bg+c
g^2+bg+(b/2)^2=(g+b/2)^2

this should help
let me know if you run into any problems