x=x0，y=y0/2。
Because P(x0, y0) is on the circle x2+y2 = 4, x02+y02 = 4.
Substitute x0 = x and y0 = 2y into equation ①,
X2+4y2 = 4。
That is, x 2/4+y2 = 1.
So the trajectory of point M is an ellipse (as shown in the figure).
Description:
① When solving the trajectory equation of point M(x, y), we don't directly establish the equation about the relationship between x and y, but first look for the relationship between x and y and the intermediate variables x0 and y0, and get the equation about the relationship between x and y by using the known equation about x0 and y0. This method of solving the locus equation of points by using intermediate variables is a common method in analytic geometry.
(2) If the equation of the locus of a point is the same as the standard equation of an ellipse, the locus is an ellipse.
It can be seen from the conclusion of this problem that an ellipse can be obtained by uniformly compressing (elongating) a circle in a certain direction.