平面直角坐标系
复平面
1. 直线的参数方程
{ x = x 0 + t cos α y = y 0 + t sin α (t为参数)
z = z 0 + t z 1 ( z 1 = cos α + i sin α , z 0 = x 0 + i y 0 ) (t为参数)
2. 圆的参数方程
{ x = x 0 + R cos θ y = y 0 + R sin θ ( 0 ≤ θ ≤ 2 π ) ( θ 为参数)
z = z 0 + t R ( t = cos θ + i sin θ , z 0 = x 0 + i y 0 , 0 ≤ θ ≤ 2 π ) (t为参数)
3. 椭圆的参数方程
{ x = x 0 + a cos θ y = y 0 + b sin θ ( 0 ≤ θ ≤ 2 π ) ( θ 为参数)
z = z 0 + t ( t = a cos θ + i b sin θ , z 0 = x 0 + i y 0 , 0 ≤ θ ≤ 2 π ) (t为参数)
4. 双曲线的参数方程
{ x = x 0 + a sec θ y = y 0 + b tan θ ( θ 为参数)
z = z 0 + t ( t = a sec θ + i b tan θ , z 0 = x 0 + i y 0 ) (t为参数)
5. 抛物线的参数方程
{ x = 2 p t 2 y = 2 p t (t为参数)
z = 2 p z 0 ( z 0 = t 2 + i t ) ( z 0 为参数)