What is the undetermined coefficient method Ditto (detailed)

In this paper, a polynomial is expressed as a new form with undetermined coefficients, and an identity is obtained. Then, according to the nature of the identity, the equation or system of equations that the coefficients should satisfy is obtained. Then, by solving the equation or system of equations, the undetermined coefficients can be obtained, or the relations that some coefficients satisfy can be found

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1. Given that the equation of circle O is x ^ 2 + y ^ 2 = 9, find the locus of the middle point P of the circle passing through the chord of point a (1,2)? Given that the equation of circle O is x ^ 2 + y ^ 2 = 9, find the locus of the midpoint P of the chord of the circle passing through point a (1,2)? Thank you
2. It is known that the radius of the center (0,2) of the circle m is 1, q is the moving point on the x-axis, QA and QB are tangent to the circle m, a and B respectively Finding the trajectory equation of the midpoint P of the moving string ab It's on the Internet, but I can't understand it, Well, 50 more points!
3. The trajectory equation () of the midpoint of each chord passing through a point P (1,1) in the circle (X-2) ^ 2 + (Y-2) ^ 2 = 4? (x-3 / 2) ^ 2 + (Y-3 / 2) ^ 2 = 1 / 2 (in known circle)
4. In the circle x2 + y2 = 9, the trajectory equation of the midpoint of the moving chord of known point P (1,2) is_________
5. Mathematics of senior one: given that BC is a moving chord of circle x ^ 2 + y ^ 2 = 25 and / BC / = 6, then the trajectory equation of the midpoint of BC is?
6. Given that the equation of circle O is the square of X + the square of y = 9, find the trajectory equation of the midpoint P of the chord of the circle through point a (1,2)?
7. High school mathematics, equations of straight line and circle 1. Draw a tangent line from a point P (2,3) outside the circle (x-1) ^ 2 + (Y-1) ^ 2 = 1 to the circle and find the tangent equation 2. Find the area of the figure enclosed by the curve X ^ 2 + y ^ 2 = / X / + / Y /
8. "M = 1 / 2" means that the line (M + 2) x + 3My + 1 = 0 is perpendicular to the line (m-2) x + (M + 2) Y-3 = 0 A. Necessary and sufficient conditions B. Sufficient and unnecessary conditions C. Necessary and insufficient conditions D. Unnecessary and insufficient conditions I want to choose a, but I don't think it's right,
9. On the equation of line and circle in high school mathematics 1. Why can two linear equations be established simultaneously to obtain the linear system equation of the intersection of two lines? It is the derivation of the formula ax + by + C + n (AX + by + C) = 0. 2. There are three methods to find the chord length of a circle, one of which is obtained by using the root and coefficient of the quadratic equation of one variable. A linear equation and a circular equation are established simultaneously, and after elimination, we can get X1 + X2, X1 * x2 or Y1 + Y2, The relation of Y1 * Y2, and then the absolute value of chord length = what under the root sign (can't be typed out). How do you get this?
10. Given the circle x 2Y 2-6x-55 = 0, the moving circle m passes through the fixed point a (- 3,0) and is tangent to the known circle, the trajectory equation of the center m is obtained
11. Equation of circle (on line, etc.) In XY coordinates, the radius r of the circle point at C (0,10) is 190, and there is a point B at the intersection of the circle point and the positive half axis of the X axis. When the point B moves on the X axis, the trajectory of the origin C is relatively fast~ In XY coordinates, the radius r of the circle point at C (0, a) is 190, and there is a point B at the intersection of the circle point and the positive half axis of the X axis. When the point B moves on the X axis, the trajectory of the origin C is the same. It's urgent~
12. The equation for finding a circle An equation for finding a circle with diameter a (- 4,0) B (0,2)
13. Seeking: the equation of circle High school students, know the equation of the circle, please write down in the walk! Must want this formula, thank you ha!
14. What is the equation for a circle?
15. 1) Try to find the circular equation through three known points （1,1）（2,-1）（3,2） 2) A circle and two parallel lines 2x + y = 5 are tangent to 2x + y + 15 = 0 and pass through point (2,1) Find the equation for this circle 3) A circle passes through (1,1) and (1, - 1) and is tangent to the straight line X - 2 = 0. Find the equation of the circle 4) Try to find the parameter equation of circle x ^ 2 + y ^ 2-x-3y = 0 5) Try to find the circular equation with the diameter of the line between (2, - 5) and (8, - 1), and find the parametric equation of this circle 20 points for answering one question
16. The equation of the circle passing through the point a (0,5) B (1, - 2) C (- 3, - 4) is solved by the method of undetermined coefficient, and D E F is calculated first
17. The general steps of finding the analytic expression of function by undetermined coefficient method Be specific
18. The main process of applying the method of undetermined coefficient to solve elliptic standard equation is?
19. Detailed steps of matching method and undetermined coefficient method (undetermined coefficient method should have examples) Given the function f (x-1) = x ^ 2-3x + 2, find f (x + 1) Please use the matching method to list the detailed steps, because I don't know how 2 - (x-1) in step f (x + 1) ^ 2 - (x-1) comes from There are also the detailed steps of undetermined coefficient method (please work out an example for me) It's really troublesome. But thank you for 80
20. How to find the equation of a circle symmetric to a line?