Ellipses Conic Sections

  • Ellipses Conic Sections

  • lLammar Academy

    lLammar Academy

    Organizer
    April 14, 2021 at 1:00 pm

    What are the features of an ellipse?

    \small\blueD{\text{Center}}Center\small\greenD{\text{Vertex}}Vertex\small\greenD{\text{Vertex}}Vertex\small\purpleC{\text{Co-vertex}}Co-vertex\small\purpleC{\text{Co-vertex}}Co-vertex\small\maroonC{\text{Focus}}Focus\small\maroonC{\text{Focus}}Focus

    An ellipse has two radii of unequal size: the \greenD{\text{major radius}}major radiusstart color #1fab54, start text, m, a, j, o, r, space, r, a, d, i, u, s, end text, end color #1fab54 is longer than the \purpleC{\text{minor radius}}minor radiusstart color #aa87ff, start text, m, i, n, o, r, space, r, a, d, i, u, s, end text, end color #aa87ff. In our example, the major radius is the horizontal one, but that could be otherwise.

    The \greenD{\text{major axis}}major axisstart color #1fab54, start text, m, a, j, o, r, space, a, x, i, s, end text, end color #1fab54 connects the ellipse’s \greenD{\text{vertices}}verticesstart color #1fab54, start text, v, e, r, t, i, c, e, s, end text, end color #1fab54, and the \purpleC{\text{minor axis}}minor axisstart color #aa87ff, start text, m, i, n, o, r, space, a, x, i, s, end text, end color #aa87ff connects the ellipse’s \purpleC{\text{co-vertices}}co-verticesstart color #aa87ff, start text, c, o, negative, v, e, r, t, i, c, e, s, end text, end color #aa87ff. The axes are twice the size of their corresponding radii.

    The \blueD{\text{center}}centerstart color #11accd, start text, c, e, n, t, e, r, end text, end color #11accd of the ellipse lies at the midpoint of its \greenD{\text{vertices}}verticesstart color #1fab54, start text, v, e, r, t, i, c, e, s, end text, end color #1fab54, which is also the midpoint of its \purpleC{\text{co-vertices}}co-verticesstart color #aa87ff, start text, c, o, negative, v, e, r, t, i, c, e, s, end text, end color #aa87ff.

    The \maroonC{\text{foci}}focistart color #ed5fa6, start text, f, o, c, i, end text, end color #ed5fa6 of the ellipse lie on the \greenD{\text{major radius}}major radiusstart color #1fab54, start text, m, a, j, o, r, space, r, a, d, i, u, s, end text, end color #1fab54. Their special property is that the sum of the distances from the foci to each point on the ellipse is always the same.

    Want to learn more about ellipses? Check out this video.

    Check your understanding

    PROBLEM 1

    \small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}-4\small{\llap{-}5}-5\small{\llap{-}6}-6\small{\llap{-}7}-7\small{\llap{-}8}-8\small{\llap{-}9}-9\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}-4\small{\llap{-}5}-5\small{\llap{-}6}-6\small{\llap{-}7}-7\small{\llap{-}8}-8\small{\llap{-}9}-9yyxx

    What is the center of the ellipse?

    Choose 1 answer:

    Choose 1 answer:

    (Choice A)

    A

    (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis

    (Choice B)

    B

    (-2,0)(−2,0)left parenthesis, minus, 2, comma, 0, right parenthesis

    (Choice C)

    C

    (0,-2)(0,−2)left parenthesis, 0, comma, minus, 2, right parenthesis

    (Choice D)

    D

    (0,-3)(0,−3)left parenthesis, 0, comma, minus, 3, right parenthesis

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Original Post
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