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Math Help - Analytic Geometry - General Equation of a Circle - please check my work

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    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
    Last edited by Principia11; December 27th 2011 at 10:08 AM.
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    Re: Analytic Geometry - General Equation of a Circle - please check my work

    Quote Originally Posted by Principia11 View Post
    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
    12+4+9=25
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    Re: Analytic Geometry - General Equation of a Circle - please check my work

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

    That's correct.
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    Re: Analytic Geometry - General Equation of a Circle - please check my work

    Quote Originally Posted by Principia11 View Post
    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
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