Correlation point method (substitution method): use the coordinates X and Y of moving point Q to represent the coordinates x0 and y0 of related point P, and then substitute them into the curve equation satisfied by the coordinates (x0 and y0) of point P, and get the trajectory equation of moving point Q simply and clearly. This method of solving trajectory equation is called correlation point method. If the movement of the moving point P is caused by the movement of another point P'.
The motion law of this point is known (the coordinates of this point satisfy a known curve equation), so we can set P(x, y), use (x, y) to represent the coordinates of the related point p', and then substitute the coordinates of p' into the known curve equation to get the trajectory equation of the moving point p.
Moving point problem in mathematics
1, the origin of a number axis is O, and the number corresponding to point A is-1 12, and point A translates evenly along the number axis through the origin to point B. ..
(1) If OA=OB, what is the number corresponding to point B? (2) It takes 3 seconds from point A to point B, and find the moving speed of this point.
(3) It takes 9 seconds to move from point A to point C at a uniform speed along the number axis, KC=KA, and the numbers corresponding to point K and point C are calculated respectively. ?
2. Moving point A moves from the origin to the negative direction of the number axis, and moving point B also moves from the origin to the positive direction of the number axis. After 3 seconds, the distance between two points is 15 unit lengths. It is known that the speed ratio of moving points A and B is 1: 4. (Speed unit: unit length/second)
(1) Find the speed of two moving points, and mark the positions of point A and point B when they move from the origin for 3 seconds on the number axis;
(2) If the two points A and B move from the position in (1) to the negative direction of the number axis at the same time, the origin will be right in the middle of the two moving points in a few seconds;
(3) In (2), when point A and point B continue to move in the negative direction of the number axis at the same time, another moving point C starts from the position of point B and moves to point A at the same time. When it meets point A, it immediately returns to point B, then moves to point A, and so on, until B catches up with point A, and C immediately stops moving. If point C keeps moving at a constant speed of 20 unit length/second, then point C starts to stop.