Thread: 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.

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

Where's in the equation? A polar equation looks like: but I don't see anywhere.

Originally Posted by Siron

Where's in the equation? A polar equation looks like: but I don't see 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.

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.

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

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