Thread: Analytic Geometry - General Equation of a Circle - please check my work

I am trying to teach myself analytic geometry and ran across a book with lots of problems but unfortunately it does not have a lot of answers. So can you guys please check my work and tell me if I got anything wrong (and where I got something wrong).

Thanks!

1. "Find the center and radius of each of the following circles"

x^2 + y^2 - 4x + 6y = 12

I rearranged the terms, added parentheses and then added the squaring terms:

(x^2 - 4x +4) + (y + 6y + 9) = 12

then added 9 + 4 to 12, and then arranged the equation in the squared form to get

(x-2)^2 + (y-(-3))^2 = 25

so r = sqrt(25)
and the center is: 2,-3

Please check my work

Originally Posted by Principia11

1. "Find the center and radius of each of the following circles"
x^2 + y^2 - 4x + 6y = 12
I rearranged the terms, added parentheses and then added the squaring terms:

(x^2 - 4x +4) + (y + 6y + 9) = 12

then added 9 + 4 to 12, and then arranged the equation in the squared form to get
(x-2)^2 + (y-(-3))^2 = 23

sorry >.< wrote it wrong once and then just copied from there, forgot to check it multiple times... except for that is it right? so r = 5 ?

That's correct.

Originally Posted by Principia11

I am trying to teach myself analytic geometry and ran across a book with lots of problems but unfortunately it does not have a lot of answers. So can you guys please check my work and tell me if I got anything wrong (and where I got something wrong).

Thanks!

1. "Find the center and radius of each of the following circles"

x^2 + y^2 - 4x + 6y = 12

I rearranged the terms, added parentheses and then added the squaring terms:

(x^2 - 4x +4) + (y + 6y + 9) = 12 + 4 + 9

then added 9 + 4 to 12, and then arranged the equation in the squared form to get

(x-2)^2 + (y-(-3))^2 = 25

so r = sqrt(25)
and the center is: 2,-3

Please check my work

Correcting that middle step (if you add something to one side, you have to do it to the other), then everything is correct