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Math problem solving in senior high school entrance examination!
The answer to the second question is incorrect. The hyperbola y=k/x should be changed.

Solution: Let the coordinates of point A be (a, k/a) and point B be (2a, k/2a).

The coordinates of c are set to (x, 0). Because of the ABC line.

So there is (0-k/a)/(x-a)=(k/2a? -? k/a)? /(2a-a)

The solution is x=3a.

S△AOC= 1/2*? Supervisor *(k/a)

= 1/2*3a*k/a=6

So k=4