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Math Help - parabolas

  1. #1
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    Help PLease!!

    1. Find the equation of a parabola with vertex at (1,5) and focus (-5.5).

    2. Find the equation of an ellipse with endpoints of the minor axis (10,2) and (10,8) and major axis of length 24.
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  2. #2
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    Quote Originally Posted by Brooke
    1. Find the equation of a parabola with vertex at (1,5) and focus (-5.5).
    2. Find the equation of an ellipse with endpoints of the minor axis (10,2) and (10,8) and major axis of length 24.
    Hello, Brooke,

    1. I assume that there is typo and you actually mean that the focus has the coordinates (-5,5).

    2. The general equation of a parabola with axis parallel to the coordinate axis is:
    (y-y_V)^2=2\cdot p \cdot (x-x_V) where p is the distance between the focus and the directrix. So plug in the values you know and you'll get:

    (y-5)^2=2\cdot (-12) \cdot (x-1)

    3. The axises of the ellipse are parallel to the coordinate axises. The centre of the ellipse is thus M(10,5). So the endpoints of the major axis are at L(-2,5) and R(22,5)

    Greetings

    EB
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