I need some help

Question

What is the polar equation for the curve represented by the equation y = 1 + 3x?

A. (1/sinθ - 3cosθ, 0)

B. (1/sinθ + 3cosθ, 0)

C. (1/3sinθ - cosθ, 0)

D. (1/3sinθ + cosθ, 0)

Answer 1

The conversion of rectangular to polar uses:

x = r•cos(θ)

y = r•sin(θ)

So just substitute these into y = 1 + 3x and it turns into:

r•sin(θ) = 1 + 3r•cos(θ)

To turn this into a function r(θ) just solve for r:

r•sin(θ) - 3r•cos(θ) = 1

r(sin(θ) - 3cos(θ)) = 1

r = 1/(sin(θ) - 3cos(θ))