A line whose perpendicular from the origin has length d and makes an angle α with the x-axis:
r cos(θ − α) = d
Example ① Find the polar equation of the line x = 3.
Solution: Since x = r cosθ, r cosθ = 3
Solution: Since x = r cosθ, r cosθ = 3
Key Point
- Substitute x = r cosθ and y = r sinθ, then rearrange in terms of r.
Practice Problems
- Find the polar equation of the line y = 2.
Solutions and Explanations
- Solution: r sinθ = 2