What are the solutions to the moving point trajectory problem?

1. The basic steps of finding the trajectory equation of the moving point.

Establish an appropriate coordinate system.

set the coordinates of the departure point m;

Write out the set of points m;

list equation=0;

Simplifying the equation to its simplest form;

Inspection. <>

2. Common methods for finding the trajectory equation of the moving point:

There are many methods to find the trajectory equation, and the commonly used ones are literal translation method, definition method, correlation point method, parameter method and intersection method.

Definition method: If the trajectory of the moving point can be determined to meet the definition of a known curve, the equation can be written using the definition of the curve, and this method of finding the trajectory equation is called the definition method.

Correlation point method: The coordinates x,y of the perturbation rubber point q are used to represent the coordinates x0 and y0 of the correlation point p, and then the curve equation satisfied by the coordinates of the point p (x0, y0) is substituted to obtain the trajectory equation of the moving point q easily, and this method of finding the trajectory equation is called the correlation point method.

Parameter method: when the direct relationship between the coordinates of the moving point x and y is difficult to find, the relationship between x and y and a variable t is often found first, and then the parametric variable t is eliminated to obtain the equation, which is the trajectory equation of the moving point, and this method of finding the trajectory equation is called the parameter method.

Cross-orbit method: The parameters in the two-motion curve equation are eliminated to obtain an equation without parameters, that is, the trajectory equation of the intersection point of the two-motion curve, and this method of finding the trajectory equation is called the cross-orbit method.

A plexus guessing method for finding the trajectory equation of the moving point.

1) Direct method - if the law of motion of the moving point is the equivalence relationship of some geometric quantities, and these conditions are simple, clear and easy to express, then the equation can be directly listed according to the known (or findable) equivalence relationship. Seepage type.

2) Pending coefficient method - If the type of curve cover and the specific form of the equation can be known from the known conditions, the pending coefficient method can generally be used.

3) Substitution method (or correlation point method) - sometimes the geometric condition satisfied by the moving point p is not easy to find, but it moves with the motion of another moving point p, which is called the relevant point, and if the condition satisfied by the relevant point p is simple and clear (or the trajectory equation of p is known), the moving point p can be used. The coordinates represent the coordinates of the relevant point p, and then the trajectory equation satisfied by the relevant point is expressed by the condition (or the coordinates of the relevant point are substituted into the known trajectory equation) to obtain the trajectory equation of the moving point.

4) Parameter method - sometimes it is difficult to directly find out the relationship between the horizontal and vertical coordinates of the moving point, you can choose a (sometimes given) parameter related to the coordinates of the moving point x, y, and use this parameter to represent x, y, and then eliminate the parameter method.

Task Type 1: Use the direct method to find the curve equation.

Task Type 3: Use the correlation point method to find the curve equation.

Task Type 4: Use the parametric method to find a curve equation.

Commonly used methods include direct method, definition method, substitution method, parameter method, etc.