Sketch the curve given in polar coordinates by the equation:

r= (2a) / (3+2cos x)

Prove that this curve is an ellipse and identify its foci.

*From a Further pure maths book.

Thanks brothers.

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- Jul 23rd 2011, 07:33 AMkakatomya question about ellipse
Sketch the curve given in polar coordinates by the equation:

r= (2a) / (3+2cos x)

Prove that this curve is an ellipse and identify its foci.

*From a Further pure maths book.

Thanks brothers. - Jul 23rd 2011, 10:34 AMwaqarhaiderRe: a question about ellipse
your equation can be arranged as

r = (2a/3) / [1 + (2/3)cos x] now comparing with polar equation of conic r = l / ( 1 + ecos x)

we get eccentricity e = 2/3 < 1 so represent ellipse with foci at pole and ( 2a,pi ) where l = 2a/3 is semi latusrectum - Jul 23rd 2011, 12:46 PMSironRe: a question about ellipse
Where's $\displaystyle \theta$ in the equation? A polar equation looks like: $\displaystyle r=f(\theta)$ but I don't see $\displaystyle \theta$ anywhere.

- Jul 23rd 2011, 10:45 PMkakatomyRe: a question about ellipse
- Jul 23rd 2011, 10:48 PMkakatomyRe: a question about ellipse
r = l / ( 1 + ecos x)

the ' l ' means?

i am not good at maths. not reli understand the idea, thanks brother helping me to further explain. thanks. - Jul 24th 2011, 10:43 AMwaqarhaiderRe: a question about ellipse
$\displaystyle r=\frac{l}{1-ecos\Theta}$

is polar equation of conic and represent ellipse if e<1 with foci at

$\displaystyle \Theta=0$ and$\displaystyle \Theta=\pi$ - Jul 24th 2011, 11:29 AMSironRe: a question about ellipse
If you want to work with latex you have to use [ tex ] ... [/ tex], not [ Tex] ... [/ Tex ]