Question

How do you graph `r = 4 / (2+sinΘ)`?

Answer 1

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)#..