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Math Help - find the equation

  1. #1
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    find the equation

    Find the equation of the parabola with vertex: (0,0); axis: x axis; length of latus rectum: 5.

    Please help me and show the solution... Or just give me an idea on how to answer this question... Thanks!
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  2. #2
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    Hello, lance!

    Find the equation of the parabola with:
    . . [1] Vertex: (0,0)
    . . [2] Axis: x-axis
    . . [3] Length of latus rectum: 5

    From [1], the vertex is at the Origin.
    . . The equation is of the form: . x^2 \,=\,4py\,\text{ or }\,y^2\,=\,4px

    From [2], the parabola is "horizontal": . \supset\text{ or } \subset
    . . The equation is of the form: . y^2 \:=\:4px .(a)

    From [3], the length of the latus rectum is 5.
    We are expected to know that the length of the latus rectum is 4p.
    . . Hence: . 4p = 5

    Substitute into (a): . y^2 \:=\:5x


    But the parabola can open to the left or the right.

    . . Therefore: . y^2 \;=\;\pm5x

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