How to change the general equation of a curve into a parametric equation? Mainly speaking, this question is just an example, and it doesn't matter if you don't understand it. Thank you all.

The method of transforming space curve into parametric equation is as follows: Let the general equation of space curve be F(x, y, z)=0 and G(x, y, z)=0, so that any one of x, y or z can get a suitable parametric equation for simplification.

For example, z=f(t), and then bring back the general equation of F(x, y, z)=0, and get F 1(x, y)=f 1(t), g1(.

Polar coordinate is also a form of parametric equation. For example, let x=rcosθ and y=rsinθ in the curve, and get the parameter equation r=f(θ).

Mathematical parameter equation formula

1, the parametric equation of the circle

X=a+r, cosθy=b+r, sinθ(a, b) is the center coordinate, r is the radius of the circle, and θ is the parameter.

2. Parametric equation of ellipse

X=a, cosθy=b, sinθa is the length of the long semi-axis, b is the length of the short semi-axis, and θ is the parameter.

3. Parametric equation of hyperbola

X=a, secθ (secθ) y=b, tanθa is the real semi-axis length, b is the imaginary semi-axis length, and θ is the parameter.

4. Parametric equation of parabola

X = 2pt 2, y=2pt, p represents the distance from the focus to the directrix, and t is the parameter.

5. Parametric equation of straight line

X=x'+tcosa, y=y'+tsina, x', y' and a represent straight lines passing through (x', y'), the inclination angle is a, and t is the parameter.