A circle centered at the origin with radius r: x = r cosθ, y = r sinθ（0 ≦ θ ≦ 2π）
Ellipse x²/a² + y²/b² = 1: x = a cosθ, y = b sinθ
Example ① What figure is represented by x = 3cosθ and y = 4sinθ?
Solution: (x/3)² + (y/4)² = 1 → ellipse x²/9 + y²/16 = 1
Solution: (x/3)² + (y/4)² = 1 → ellipse x²/9 + y²/16 = 1
Key Point
- Eliminate the parameter using cos²θ + sin²θ = 1.
Practice Problems
- What figure is represented by x=cosθ−1 and y=sinθ+2?
Solutions and Explanations
- Solution: A circle with center (−1,2) and radius 1