How do you graph #r = 4 / (2+sinΘ)#?

1 Answer
A. S. Adikesavan
Jun 28, 2016

This is of the form #2/r=1+(1/2)cos(pi/2-theta)# representing the ellipse with a focus at the pole r =0, major axis along #theta= pi/2, and theta=-pi/2# for the other end. #e=1/2 and a=8/3#....

Explanation:

Remodeling to the standard form

#2/r=1+(1/2)cos(pi/2-theta)#,

it is easy to see that this represents the ellipse with

a focus at the pole r = 0.

The major axis is along

#theta=pi/2#, for the non-center side and #theta=-pi/2#, for the

center-side.

The parameters #e = 1/2 and l = a(1-e^2)=a(3/4)=1/2#. So, #a = 8/3#

The center is at (ae, -pi/2)=(4/3, -pi/2)#..

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