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Math Help - Parametric and implicit equation help

  1. #1
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    Parametric and implicit equation help

    I am trying to do a couple of implicit and parametric problems for hyperbolas, ellipses and circles.

    I must be confusing myself because I think I am missing a concept.

    Problem#1: x^2+2x+y^2=0

    For the implicit equation I go to the step

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

    I then complete the square to get

    (x-1)^2 + (y-0)^2 =1

    Which I put into the form

    ((x-1)^2)/1^2 + ((y-0)^2)/1^2 =1

    from the above implicit equation it appears to be an ellipse with A=1, B=1, H=1, K=0, Center= (1,0) And parametric equation of x=1+1cosT, y=0+1sinT

    Question #1 I feel like I am doing something wrong, I believe I got 1 on the right side of the equation because of (?) not entirely sure.

    Problem #2: 2x^2+2y=y^2+4x

    For the implicit equation I bring the right side over to the left

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

    I then factor

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

    Divide the 2 out of both sides and complete the squares

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

    put it in the final form

    ((x-1)^2)/1^2 - ((y-1)^2)/1^2 =1

    From the implicit equation it appears to be a hyperbola opening left and right
    A=1, B=1, Center= (1,1), Parametric equation of x=1+1secT, y=1+1tanT




    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by oriont View Post
    I am trying to do a couple of implicit and parametric problems for hyperbolas, ellipses and circles.

    I must be confusing myself because I think I am missing a concept.

    Problem#1: x^2+2x+y^2=0

    For the implicit equation I go to the step

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

    I then complete the square to get

    (x-1)^2 + (y-0)^2 =1

    Which I put into the form

    ((x-1)^2)/1^2 + ((y-0)^2)/1^2 =1

    from the above implicit equation it appears to be an ellipse with A=1, B=1, H=1, K=0, Center= (1,0) And parametric equation of x=1+1cosT, y=0+1sinT

    Question #1 I feel like I am doing something wrong, I believe I got 1 on the right side of the equation because of (?) not entirely sure.

    Problem #2: 2x^2+2y=y^2+4x

    For the implicit equation I bring the right side over to the left

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

    I then factor

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

    Divide the 2 out of both sides and complete the squares

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

    put it in the final form

    ((x-1)^2)/1^2 - ((y-1)^2)/1^2 =1

    From the implicit equation it appears to be a hyperbola opening left and right
    A=1, B=1, Center= (1,1), Parametric equation of x=1+1secT, y=1+1tanT




    Any help would be appreciated.
    x^2 + 2x + y^2 = 0

    x^2 + 2x + 1 + y^2 = 1

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

    --------------------------------------

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

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

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

    2(x-1)^2 - (y-1)^2 = 1
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  3. #3
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    Quote Originally Posted by skeeter View Post
    x^2 + 2x + y^2 = 0

    x^2 + 2x + 1 + y^2 = 1

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

    --------------------------------------

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

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

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

    2(x-1)^2 - (y-1)^2 = 1
    The only problem is it is supposed to be in the form [(x-h)2]/a^2 + [(y-k)^2)]/a^2
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  4. #4
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    Quote Originally Posted by oriont View Post
    The only problem is it is supposed to be in the form [(x-h)2]/a^2 + [(y-k)^2)]/a^2
    It should be obvious that a = b = 1 in the first. And in the second a = 1/sqrt{2} and b = 1.
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