# Homework Help: The radius of an ellipse from the origin.

1. Mar 21, 2008

### Erez

Hello,
given (x^2)/(a^2) + (y^2)/(b^2) = 1.
and using polar coordinates x=rcos(phi) , y=rsin(phi),
equating gives r^2 = 1/[(cos^2(phi)/a^2) + (sin^2(phi)/b^2)].
or if we leave b in the nominator :
r= b/[(sin^2(phi)+(b^2/a^2)cos^2(phi)]^1/2.

-could someone give a hint as to how the demoninator of the last expression can be turned into [1 - (e^2)cos^2(phi)]^1/2 where e is the eccentricity of the ellipse?
and what is the value of e?

thank you.

Last edited: Mar 21, 2008
2. Mar 21, 2008

$$e^2=1-\frac{b^2}{a^2}$$

And by the way this is introductory physics section.

3. Mar 21, 2008

### tiny-tim

Welcome to PF!

Hi Erez! Welcome to PF!

Hint: use cos^2(phi) + sin^(phi) = 1.

Then … ?

4. Mar 21, 2008

### Erez

Hello,
I am surprised I recived a reply so quick,
thank you.
p.s. in what category/section would this post belong ?

5. Mar 21, 2008