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Math Help - circle

  1. #1
    Member
    Joined
    Aug 2009
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    211

    circle

    hi,

    write down the equation of the circle which is obtained by applying the given translation to the given circle:

    [1, 0] x^2 + y^2 + 4x - 2y = 2

    i first started by rearranging the equation into:
    (x + 2)^2 - 4 + (y - 1)^2 - 1 = 2 and then
    (x + 2)^2 + (y - 1)^2 = 7 and then translate it
    (x + 1)^2 + (y - 1)^2 = 7

    but the books answer is x^2 + y^2 + 2x - 2y = 5

    can someone show me the steps to arriving at that answer please and also where i went wrong with mine? thanks
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  2. #2
    MHF Contributor Amer's Avatar
    Joined
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    Jordan
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    Quote Originally Posted by mark View Post
    hi,

    write down the equation of the circle which is obtained by applying the given translation to the given circle:

    [1, 0] x^2 + y^2 + 4x - 2y = 2

    i first started by rearranging the equation into:
    (x + 2)^2 - 4 + (y - 1)^2 - 1 = 2 and then
    (x + 2)^2 + (y - 1)^2 = 7 and then translate it
    (x + 1)^2 + (y - 1)^2 = 7

    but the books answer is x^2 + y^2 + 2x - 2y = 5

    can someone show me the steps to arriving at that answer please and also where i went wrong with mine? thanks
    (x + 2)^2 - 4 + (y - 1)^2 - 1 = 2 and then
    (x + 2)^2 + (y - 1)^2 = 7 and then translate it
    (x + 1)^2 + (y - 1)^2 = 7
    just simplify the power i.e

    (x+1)^2+(y-1)^2 = 7

    x^2+2x+1+y^2-2y+1 = 7

    x^2+2x+y^2-2y = 7-2=5
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