Find the values of e,a,b,and c for r=21/5-2costheta?

Answer 1

I assume you mean

r = 21/(5-2cosθ)

When you consider the general equation for a conic:

r = ep/(1 - e cosθ)

you see that you must set it up as

r = 21/[5(1 - 2/5 cosθ))

Now you can read off e and p. Since e<1, you have an ellipse. Now you need to use the distance to the directrix to determine a; then e will give you b and c.