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Math Help - ellipse

  1. #1
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    ellipse

    an ellipse has the following points

    (-2,3) left
    (2,5) top
    (6,3) right
    (2,1) bottom

    write the equation in general and standard form of the ellipse
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by dan123 View Post
    an ellipse has the following points

    (-2,3) left
    (2,5) top
    (6,3) right
    (2,1) bottom

    write the equation in general and standard form of the ellipse
    The length of the axis are as follows:

    Between \left(-2,3\right),\left(6,3\right): length is 6-(-2)=8
    Between \left(2,5\right),\left(2,1\right): length is 5-1=4

    So it follows that the major axis is parallel to the x axis and a=4, and the minor axis is parallel to the y axis and b=2.

    The ellipse will take the form \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1.

    I leave it for you to verify that the center of the ellipse is (2,3).

    Therefore, the equation of the ellipse is \frac{(x-2)^2}{16}+\frac{(y-3)^2}{4}=1

    Does this make sense?
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  3. #3
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    yeah,it does,I knew the formulas and everything,but I just find it difficult to put it all together
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