# Thread: [SOLVED] Proof of algebra for ellipse

1. ## [SOLVED] Proof of algebra for ellipse

Hello.
This is the same problem for me

http://www.mathhelpforum.com/math-he...f-ellipse.html

I find the same values of:

a=5
b=sqrt(15)
Foci: + and - (sqrt(10), 0)
Directrices: + and - 5*sqrt(10)/2
Eccentricity: sqrt(10)/5
Center: (0,0)
Vertices: (5,0) (-5,0) (0, sqrt(15)), (0, -sqrt(15))

I only worry about the PF=ePd part of the question.

Does not this mean P * F = e * P * d?

When I am putting all of the numbers in the equation then the two sides are not being equal. My answer is:

(5 * sqrt(10) = sqrt(10)/5 * 5 * 25/sqrt(10)

so that (5 * sqrt(10) = 5 * sqrt(10)/2

When I look at the above link, they are using different equations (where do they find this?) and the answers result differently. They use

PF = a-ae = $\displaystyle -5+\sqrt{10}$
and ePd = e(a-ae)/e = $\displaystyle \sqrt{10}/5\times(-5+\sqrt{10}/\sqrt{10}/5$
= $\displaystyle -5+\sqrt{10}$

This is not like I have. How must I find "PF =a-ae" and "ePd=e(a-ae)/e"? It is not in my book and I am not finding it on the internet.

My sides don't balance. The sides of him balance!

Hope someone is not busy to help me!
Brigitte

2. Now I have solved this.

Thanks.