SOLUTION: one question: about finding center and radius (circle graph) : {{{ 3x^2 + 3y^2 - 6x + 12y= 0 }}} i did this: (3x^2 -6x) + (3y^2 +12y)=0 then I complete the square

Question 98840This question is from textbook
: one question: about finding center and radius (circle graph) :

i did this:
(3x^2 -6x) + (3y^2 +12y)=0
then I complete the square:
-6/2 = -3^2=9 and 12/2 =6^2=36
then:
(3x^2-6x+9) + (3y^2+12y+36)= 9+36
(3x-3)^2 + (3y +6)^2 =45
factor:
3(x-1) + 3(y+2)= 45
i got the answer for center:
C(1,-2)
and the answer to the raduis is square root of 5
which i dont know how they got it.

thank you

This question is from textbook

Found 3 solutions by stanbon, scott8148, Earlsdon:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find center and radius:
3x^2 + 3y^2 - 6x + 12y= 0
Divide thru by 3 to get:
x^2+y^2-2x+4y=0
Complete the square on the x-terms and y-terms separately:
x^2-2x+1 + y^2+4y+4 = 1+4
(x+1)^2 + (y+2)^2 = 5
--------------
Center at (-1,-2)
Radius = sqrt(5)
===============
Cheers,
Stan H.
Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
the first step in completing the square should be to make the coefficient of the squared term 1

in this case, the first step is to factor (reduce) if possible ... dividing by 3 gives x^2+y^2-2x+4y=0

completing the square gives x^2-2x+1+y^2+4y+4=5 ... (x-1)^2+(y+2)^2=5

if you FOIL (3x-3)^2, you don't get 3x^2-6x+9 ... similarly with (3y+6)^2
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Well, your error is found in the step..."completing the square"
Let's go over that:
then you said ..."complete the square", but before you do that, you should factor out a 3 then divide through by 3 and you will get:
Divide both sides by 3.
Now you complete the square when the coefficients of the and terms are equal to 1.
Factor the trinomials.
Now compare this with the standard form for a circle of radius r and center at (h, k).
and you can see that h = 1, k = -2, and
The center (h, k) is at (1, -2) and the radius is

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