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Math Help - Equation of ellipse question Help!

  1. #1
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    Unhappy Equation of ellipse question Help!

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    Last edited by yellow4321; March 6th 2008 at 05:25 AM.
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  2. #2
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    By definition, an ellipse is the set of points the sum of the distances to two fixed points, the foci, is a constant.
    In the complex plane if u & v are points then the distance from u to v is |u-v|.
    Because  \pm 2i are the foci we have:
    \begin{array}{l}<br />
 \left| {z - 2i} \right| + \left| {z + 2i} \right| = \left| {3 + 2i - 2i} \right| + \left| {3 + 2i + 2i} \right| \\ <br />
 \left| {z - 2i} \right| + \left| {z + 2i} \right| = 3 + \sqrt {25}  \\ <br />
 \left| {z - 2i} \right| + \left| {z + 2i} \right| = 8 \\ <br />
 \end{array}.

    Now you finish.
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  3. #3
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    so if its the sum 2a=8
    then a=4

    so 2=a^2 - b^2

    2-16=-b^2
    14=b^2

    so equation looks something like x^2/16 + y^2/14 =1 ??
    could you start me off on part b thats if im even right on part a. cheers
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  4. #4
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    You have a = 4. This gives vertices at 4i and -4i.
    You should have c = 2. This gives b^2 = 12.

    I cannot tell why you decided to use c rather than c^2 when calculating b.
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  5. #5
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    my reasoning was that c^2=foci and because i already know foci is 2i but im a complete novice at this so i assume your right.
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