1. literal translation method: If the conditions of moving point are equivalent relations of some geometric quantities, and these conditions are simple and easy to express as equations containing x and y, the trajectory equation can be obtained. This method is called literal translation. There are five steps to find the locus of moving point by direct method: establishing system, setting points, listing, simplifying and proving. The final proof can be omitted, but attention should be paid to "digging" and "filling".

2. Definition method: Using some commonly used definitions in analytic geometry (such as the definition of conic curve), the trajectory equation can be written directly from the definition of curve, or the relationship can be established from the definition of curve, so as to find the trajectory equation.

3. Method of undetermined coefficient: If the meaning of moving point trajectory has been directly told, that is, ellipse, hyperbola, parabola, circle or straight line, the method of undetermined coefficient is directly used to solve the problem according to the meaning of the question.

4. Substitution method: it is not easy to express or find the conditions that the moving point satisfies, but the moving point P(x, y) forming the trajectory moves regularly with the movement of another moving point Q(x', y'), and the trajectory of the moving point Q is given or easy to find, then x', y' can be expressed as the formula of x, y first, and then substituted into the trajectory equation of Q, but P can be sorted out.

5. Trajectory method: eliminate the parameters in the equations of two dynamic curves, and get the equation without parameters, that is, the trajectory equation of the intersection of two dynamic curves. This method of solving trajectory equation is called trajectory method.