# Equation of ellipse question Help!

• December 27th 2007, 06:48 AM
yellow4321
Equation of ellipse question Help!
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• December 27th 2007, 07:20 AM
Plato
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:
$\begin{array}{l}
\left| {z - 2i} \right| + \left| {z + 2i} \right| = \left| {3 + 2i - 2i} \right| + \left| {3 + 2i + 2i} \right| \\
\left| {z - 2i} \right| + \left| {z + 2i} \right| = 3 + \sqrt {25} \\
\left| {z - 2i} \right| + \left| {z + 2i} \right| = 8 \\
\end{array}$
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Now you finish.
• December 27th 2007, 07:44 AM
yellow4321
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
• December 27th 2007, 08:31 AM
TKHunny
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.
• December 27th 2007, 09:00 AM
yellow4321
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.