Alegbra

What are the polar forms of these rectangular equations?

a. y = 5

b. (x – 1)^2 + y^2 = 1

c. 5x + 4y = 2

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  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...

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