As shown in the figure, the straight line y = 2x moves 2 units along the positive direction of x-axis, intersects with X-axis at point a, and intersects with hyperbola y = 6 / X and hyperbola y = K / X at two points BC respectively, And the area of triangle OBC = the area of triangle OAB, K=

As shown in the figure, the straight line y = 2x moves 2 units along the positive direction of x-axis, intersects with X-axis at point a, and intersects with hyperbola y = 6 / X and hyperbola y = K / X at two points BC respectively, And the area of triangle OBC = the area of triangle OAB, K=

The equation after line translation is y = 2 (X-2),
The area of triangle OBC = 2 the area of triangle OAB, indicating that BC = 2Ab, (two triangles are of equal height, and the ratio of the area is equal to the ratio of the length of the bottom edge)
Making the vertical line of X axis from B and C is more similar, 2Ab '= B ` C`
According to the equations of hyperbola and translational straight line, we can get B '(3,0). Ab' = 1, B ` C '= 2, C' (5,0)
When x = 5 is brought into the linear equation, the coordinates of point C are (5,6)
The hyperbolic equation leads to k = 5 * 6 = 30