Question

What are the polar forms of these rectangular equations?

a. y = 5

b. (x – 1)^2 + y^2 = 1

c. 5x + 4y = 2

Answer 1

just use your normal parameterization

y=5
r sinθ = 5

(x-1)^2 + y^2 = 1
(r cosθ - 1)^2 + (r sinθ)^2 = 1
r^2 cos^2θ - 2rcosθ + 1 + r^2 sin^2θ = 1
Now that simplifies easily

5x+4y = 2
5rcosθ + 4rsinθ = 1
now just factor out the r...