Convert the polar equation to rectangular form:

r = 2 / [1 + sin (theta) ]

R = 2 / (1 + sin θ)

Using the following relations:

R = sqrt (x^2 + y^2)

sin θ = y/R

R = 2 / (1 + y/R)

R (1 + y/R) = 2

R + y = 2

R = 2 - y

sqrt (x^2 + y^2) = 2 - y

Squaring both sides:

x^2 + y^2 = (2 - y) ^2

x^2 + y^2 = 4 - 4y + y^2

x^2 + 4y - 4