1. Establishing coordinate system: First, we need to choose a suitable coordinate system to represent the position of the moving point. Common coordinate systems are Cartesian coordinate system, polar coordinate system and spherical coordinate system. Which coordinate system to choose depends on the specific nature and needs of the problem.
2. Determine the parametric equation of the moving point: the trajectory of the moving point can usually be expressed by the parametric equation. Parametric equation is a set of equations containing one or more parameters, which can be used to represent the position of a moving point in the process of motion. For example, on the two-dimensional plane, the parameter equation of the moving point can be expressed as x=x0+at, y=y0+bt, where (x0, y0) is the initial position of the moving point, and a and b are parameters related to the moving direction and speed.
3. Transforming the parametric equation into the constant equation: By eliminating the parameters, we can transform the parametric equation into the constant equation. Constant equation is an equation without parameters, which can be directly used to describe the trajectory of moving points. For example, in the above parametric equation, we can get x-x0=at and y-y0=bt by eliminating T, and then add these two equations to get X 2-2x0x+Y 2-2Y0y = 0, which is the ordinary equation of the moving point.
4. Analyze the trajectory of the moving point: By observing the constant equation, we can analyze the properties of the trajectory of the moving point. For example, if the constant equation is a circular equation, then the trajectory of the moving point is a circle; If the constant equation is an elliptic equation, then the trajectory of the moving point is an ellipse; If the constant equation is a parabolic equation, then the trajectory of the moving point is a parabola and so on. In addition, we can also determine the position of the moving point at different times by solving the constant equation, so as to further analyze the trajectory of the moving point.
5. Use analytic geometry tools to calculate: In analytic geometry, we can also use various tools (such as vectors, matrices, determinants, etc. ), thus simplifying the description and solving process of the problem. For example, we can use the cross product of vectors to calculate the angle between two vectors, so as to determine the moving direction of the moving point; We can use the inverse matrix of the matrix to calculate the derivative of the moving point, so as to analyze the speed change of the moving point.
In a word, with the help of analytic geometry, we can easily describe and analyze the trajectory of the moving point, so as to better understand and solve the problems related to the motion of the moving point.