Question

Given 4/ (-2 - cos(theta))

What is the eccentricity of the function?

Answer 1

the eccentricity is 1/2

Explanation:

Rewritten to the form ...

r = ed/(1+e·cos(theta))

you find ..

ed = 4/-2

e = -1/-2 = 1/2 . . . . . the eccentricity

so d = -4 and the ellipse has the equation ...

r = (1/2)(-4)/(1 + 1/2·cos(theta))

The eccentricity is 1/2.

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Additional comment on the geometry

The directrix is a vertical line 4 units from the focus.