Final answer:
To find the eccentricity and identify the conic section of the equation r = 2/(1 - cos(theta)), rewrite the equation in terms of x and y. Compare the resulting equation with the general form for a parabola to determine the eccentricity. If the eccentricity is equal to one, the path is a parabola.
Step-by-step explanation:
To calculate the eccentricity, we need to rewrite the equation in terms of x and y instead of polar coordinates. Using the conversion formulas x = r cos(theta) and y = r sin(theta), we have:
x = (2/(1 - cos(theta))) cos(theta) = 2cos(theta)/(1 - cos(theta))
y = (2/(1 - cos(theta))) sin(theta) = 2sin(theta)/(1 - cos(theta))
Now we can find the eccentricity by expressing x in terms of y:
x = ay^2 + by + c
Comparing the equations, we get:
a = 2/(1 - cos(theta))
b = 0
c = 0
Therefore, the eccentricity is 2/(1 - cos(theta)).
The conic section represented by this equation depends on the value of the eccentricity. If the eccentricity is equal to 1, the path is a parabola.