SOLUTION: Write an equation for the circle in standard form, the state the center and radius. X^2+y^2+12x=6y When I answered this question I got (x+6)^2+(y-3)^2=2,025, but I am not sure I g

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation for the circle in standard form, the state the center and radius. X^2+y^2+12x=6y When I answered this question I got (x+6)^2+(y-3)^2=2,025, but I am not sure I g      Log On


   

Question 937360: Write an equation for the circle in standard form, the state the center and radius. X^2+y^2+12x=6y
When I answered this question I got (x+6)^2+(y-3)^2=2,025, but I am not sure I got the radius right. Can you explain to me how you get the correct radius? Thank you!
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Adjust so all variable terms are on one side or the other side.
Complete The Square for the x and the y.
(Check the lesson for how to do Completing The Square.)


X%5E2%2By%5E2%2B12x=6y, ?
?

x%5E2%2By%5E2%2B12x=6y
x%5E2%2B12x%2By%5E2-6y=0
%28x%5E2%2B12x%29%2B%28y%5E2-6y%29=0
%28x%5E2%2B12x%2B36%29%2B%28y%5E2-6y%2B9%29=36%2B9
highlight%28%28x%2B6%29%5E2%2B%28y-3%29%5E2=45%29
or alternatively equivalent to
highlight%28%28x%2B6%29%5E2%2B%28y-3%29%5E2=%283sqrt%285%29%29%5E2%29



The radius is 3%2Asqrt%285%29