Expert: Sherry Wallin - 12/6/2008

Question
HELP!
Two precalc problems, one of which I have an answer to that does not seem right.

1. Given the circle whose center is (4,-3) and radius 6, write the equation in general form.

2. Find the center and radius of the circle:
3x^2 + 3y^2 - 6x + 18y + 18 = 0

For the second problem I attempted to complete the square and for my answers, I found the center to be (1.5 , -3) and the radius at 4.63. I am pretty sure this is not correct, as the problems were supposed to work out (somewhat) evenly.

If you could help me with this it would be GREATLY appreciated.
Thanks so much, Jen

Answer
Hi Jennifer~
    Next time show me how you worked the problem so I can tell you where you made your mistake. That is far more valuable than me just giving you the answer.

Ok, there are a few ways to do this. There is a simpler way or a more sophisticated way. I will do it the simpler way for you. Notice that the gcd = 3 so divide it out to make the numbers smaller and the coefficients on the squared terms 1.

3x^2 "+"   3y^2 - 6x "+"  18y "+"  18 = 0 becomes
x^2 "+"  y^2 - 2x "+"  6y  "+" 6 = 0
rearrange your terms so you can begin to complete the squares
x^2 - 2x "+"  (-1)^2  "+"  y^2 "+"  6y "+"  3^2 "+"  6 - 6
= -6 "+" (-1)^2 "+"  3^2
(x-1)^2 "+"  (y 3)^2 = 4
So your center is (1,-3) and the radius is 2.

Good luck!
Math Prof

Ps It is necessary to use "+" for plus because the plus sign does not show up when sending this over.