The polar equation of a conic section with its focus at the origin (eccentricity e and distance l to the directrix):
r = el/(1 − e·cosθ)
- e = 1: parabola
- 0 < e < 1: ellipse
- e > 1: hyperbola
Example ① What kind of curve is r = 2/(1 − cosθ)?
Solution: Since e=1, it is a parabola.
Solution: Since e=1, it is a parabola.
Key Point
- Determine the type of curve from the coefficient e in the denominator.
Practice Problems
- What kind of curve is r = 4/(2 − cosθ)?
Solutions and Explanations
- Solution: Ellipse (e=1/2)