.

.

Printable View

- Dec 27th 2007, 06:48 AMyellow4321Equation of ellipse question Help!
.

. - Dec 27th 2007, 07:20 AMPlato
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 $\displaystyle \pm 2i$ are the foci we have:

$\displaystyle \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}$.

Now you finish. - Dec 27th 2007, 07:44 AMyellow4321
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 - Dec 27th 2007, 08:31 AMTKHunny
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. - Dec 27th 2007, 09:00 AMyellow4321
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.