MS has a similar topic, which is said to have been recruited by Jiaotong University in 2000, as follows:

U = y 2-x 2, v = 2xy If the point (x, y) moves on y=ax+b and the point (u, v) moves on a straight line passing through the point (1, 1), find the values of a and b.

If there is, it should be simple. As long as you substitute u= 1 and v= 1, you can solve an equation group.

1=y^2-x^2

1=2xy

There are two solutions.

x 1=(√2- 1)/2

y 1=√2+ 1

x2=-(√2+ 1)/2

y2= 1-√2

Then substitute the solution of the equation into y = ax+b.

The solution is a=2 b=2.

(ps: My calculation is very poor. I don't know if there is any mistake. . . Um ... . )