What is the rectangular form of the polar equation? r−rsinθ=4
r - r·sin(theta) = 4
Since sin(theta) = y/r
r - r·(y/r) = 4
r - y = 4
Since r = sqrt(x2 + y2)
sqrt(x2 + y2) - y = 4
sqrt(x2 + y2) = y + 4
Squaring:
x2 + y2 = y2 + 8y + 16
x2 - 16 = 8y
y = 0.125x2 - 2