1. ## a 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.

2. ## Re: 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

3. ## Re: 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.

4. ## Re: a question about ellipse

Originally Posted by Siron
Where's $\displaystyle \theta$ in the equation? A polar equation looks like: $\displaystyle r=f(\theta)$ but I don't see $\displaystyle \theta$ anywhere.

sorry i dun know how to type the theta out but the x is the theta.
thanks brother.

btw hows the sketching of the curve?
i dun even know wt it is.
thanks bro.

5. ## Re: 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.

6. ## Re: 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$\displaystyle \Theta=\pi$

7. ## Re: a question about ellipse

If you want to work with latex you have to use [ tex ] ... [/ tex], not [ Tex] ... [/ Tex ]