This topic is easy to do. Let me talk about the method. It is too simple to find the analytical formula of parabola at 1, and it is known to find the analytical formula of parabola by three points. Think for yourself. (2) In the quadrilateral PAOC, three points of AOC are fixed, the minimum side length of quadrilateral is essentially the minimum value of PA+PC, and point P is on the axis of symmetry of parabola. When the point P is located at the intersection of AC and the symmetry axis PA+.

(3) According to what you said, there are countless points M. For any point Q on OB, we can make such a straight line: first pass through Q as the vertical line of OB, and then make the middle vertical line of QC. The intersection of two straight lines is naturally the point m (obviously, the angle MQB of MC=MQ is 90 degrees, that is to say, for each point Q, at least the point M that meets the conditions can be found.