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Math Help - Parabola and Foci Problems

  1. #1
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    Parabola and Foci Problems

    Hi, I need some help on these 2 problems:

    1. What is the focus of the parabola with the equation (x-1)^2+32=8y
    A. (1,4)
    B. (1,2)
    C. (-1,6)
    D. (1,6)

    2.Find the foci of an ellipse with the equation 7(x-2)^2+3(y-2)^2=21
    A. (-4, -2) and (0,-2)
    B. (-2,-4) and (-2,0)
    C. (4,2) and (0,2)
    D. (2,4) and (2,0)

    Thanks =)
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  2. #2
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    Quote Originally Posted by Alyssa21 View Post
    Hi, I need some help on these 2 problems:

    1. What is the focus of the parabola with the equation (x-1)^2+32=8y
    A. (1,4)
    B. (1,2)
    C. (-1,6)
    D. (1,6)

    2.Find the foci of an ellipse with the equation 7(x-2)^2+3(y-2)^2=21
    A. (-4, -2) and (0,-2)
    B. (-2,-4) and (-2,0)
    C. (4,2) and (0,2)
    D. (2,4) and (2,0)

    Thanks =)
    To #1:
    The general equation of a parabola opening up is:

    (x-h)^2=4p(y-k)

    The vertex of this parabola has the coordinates V(h, k) and the focus has the coordinates F(h, k+p)

    To #2:

    The general equation of an ellipse is:

    \dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1

    The center of the ellipse has the coordinates C(h, k). The focal length e is measured on the main axis (the longest of the two axes) so that the focii have the coordinates (in your case!): F_1(h, k-e), F_2(h, k+e)
    e is calculated in your case by e^2 + a^2 = b^2
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