Mathematical problems of solving trajectory equation in high school

The coordinate of point B is (0, m), and the coordinate of point A is (n, 0).

Then the slope of the straight line MB is (m-2)/(0-1) = 2-m.

The slope of the straight line NA is (0+1)/(n+1) =1/(n+1).

Because MB is perpendicular to NA, the slope product is-1.

(2-m)/(n+ 1)=- 1

2-m=-n- 1，m=3+n

The midpoint coordinate of AB is set to (x, y).

x=(0+n)/2=n/2

y=(m+0)/2=m/2

Therefore, n=2x and m=2y are obtained, and it is obtained by substituting the relationship between m and n.

2y=3+2x

The locus equation of the midpoint of AB is 2x-2y+3=0.

The whole process is (1) parameter setting; (2) Eliminating parameters