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
$\displaystyle r=\frac{l}{1-ecos\Theta}$
is polar equation of conic and represent ellipse if e<1 with foci at
$\displaystyle \Theta=0$ and$\displaystyle \Theta=\pi$