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so far:

r = 2 /(2 - cos(theta))

r = 2 /(2 - cos(theta)) |* (2 - cos(theta)) both sides

r (2 - cos(theta))= 2

2*r - rcos(theta) = 2 | know x = rcos(theta)

2*r - x = 2 | know r^2 = x^2 + y^2

2*(x^2 + y^2)^1/2 - x = 2 | : 2

(x^2 + y^2)^1/2 - x/2 = 1 | opens the parentheses

x^2*1/2 + y^2*1/2 - x/2 = 1

x + y - x/2 = 1

y = 1 - x/2 | is this the solution?

Thank you in advance for help.

Regards

sjombol