Answer:
the eccentricity is 1/2
Step-by-step 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.
