Trig

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Find a parametric equation for the ellipse. Make sure that the graph of your parametric equation is a complete ellipse.

3x^2+4y^2=12

  • Trig -

    3x^2 + 4y^2 = 12
    divide by 12
    x^2/4 + y^2/3 = 1

    we know sin^2 t + cos^2 t = 1
    so sin^2 t = x^2/4 = (x/2)^2
    ---> sin t x/s ----> x = 2sin t

    and

    cos^2 t = y^2/3 = (y/√3)^2
    cos t = y/√3
    ----> y = √3cos t

    x = 2sint
    y = √4cost

    confirmation:
    http://www.wolframalpha.com/input/?i=x+%3D+2sint+%2C+y+%3D+√3cost

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