The two ends a and B of the line segment AB with length L move on the parabola y = x ＾ 2. The midpoint of AB is m, and the shortest distance from the point m to the X axis is obtained I'm not good at math

The two ends a and B of the line segment AB with length L move on the parabola y = x ＾ 2. The midpoint of AB is m, and the shortest distance from the point m to the X axis is obtained I'm not good at math

In fact, this problem is not difficult, but it's a little troublesome to solve
Let a (x1, X1 ^ 2) B (X2, X2 ^ 2) assume that X1 > X2, have
L ^ 2 = (x1-x2) ^ 2 + (x1 ^ 2-x2 ^ 2) ^ 2 solve X1 (or x2) and bring it into the following equation
Y = 1 / 2 (x1 ^ 2-x2 ^ 2) is the minimum value of Y
Find the derivative of y = 0, solve x1, and bring the obtained value into y. The smallest is the evaluated value
Because I'm afraid I'm too tired to solve this kind of problem, I suggest that the building owner should do more questions to form his own thinking set (the teacher often tells us not to think set, but to solve the problem flexibly. My meaning here is different from that of the teacher). In fact, there are so many types of questions. When your experience reaches a certain level, the set will not be set at that time, It's like we just started learning 1 + 1 = 2