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Math Help - Find the coordinates of the center and the radius of the circle

  1. #1
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    Find the coordinates of the center and the radius of the circle

    Hey, i'm trying to solve this and im confused by the 2x and 2y. How do I treat this problem?

    Thanks guys.
    Attached Thumbnails Attached Thumbnails Find the coordinates of the center and the radius of the circle-image006.png  
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bigitme View Post
    Hey, i'm trying to solve this and im confused by the 2x and 2y. How do I treat this problem?

    Thanks guys.
    2x^2+2y^2+18x+4=0

    First divide the equation through by 2:

    x^2+y^2+9x+2=0

    Subtract 2 from both sides:

    x^2+y^2+9x=-2

    Group the x terms together:

    (x^2+9x)+y^2=-2

    Complete the square:

    \left(x^2+9x+\tfrac{81}{4}\right)+y^2=-2+\tfrac{81}{4}

    \left(x+\tfrac{9}{2}\right)^2+y^2=\tfrac{77}{4}

    Thus, the center of the circle is ........

    The radius of the circle is ........

    I hope this helps!

    --Chris
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by bigitme View Post
    Hey, i'm trying to solve this and im confused by the 2x and 2y. How do I treat this problem?

    Thanks guys.
    Your equation is:

    2x^2+2y^2+18x+4=0

    divide by 2:

    x^2+y^2+9x+2=0

    Complete the square for x:

    (x+4.5)^2+y^2+2-4.5^2=0

    so you have:

    (x+4.5)^2+y^2=4.5^2-2

    RonL
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by Chris L T521 View Post
    2x^2+2y^2+18x+4=0

    First divide the equation through by 2:

    x^2+y^2+9x+2=0

    Subtract 2 from both sides:

    x^2+y^2+9x=-2

    Group the x terms together:

    (x^2+9x)+y^2=-2

    Complete the square:

    \left(x^2+9x+\tfrac{81}{4}\right)+y^2=-2+\tfrac{81}{4}

    \left(x+\tfrac{9}{2}\right)^2+y^2=\tfrac{7{\color{  red}3}}{4}

    Thus, the center of the circle is ........

    The radius of the circle is ........

    I hope this helps!

    --Chris
    Typo!
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by masters View Post
    Typo!
    argh! Thanks for catching that

    --Chris
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