As shown in the figure, the line y = root 3x + root 3 intersects Y-axis at a and y-axis at B. rotate the line 90 ° clockwise around a certain point, and m and N are the opposite points of a and B (M and N are in the first quadrant), the line Mn intersects Y-axis at C and s △ BCM = s △ BMN, and the hyperbola y = K / X passes m and N. calculate the value of K Y = radical 3 · x + radical 3

As shown in the figure, the line y = root 3x + root 3 intersects Y-axis at a and y-axis at B. rotate the line 90 ° clockwise around a certain point, and m and N are the opposite points of a and B (M and N are in the first quadrant), the line Mn intersects Y-axis at C and s △ BCM = s △ BMN, and the hyperbola y = K / X passes m and N. calculate the value of K Y = radical 3 · x + radical 3

First, let m coordinate (x1, K / x1)
N (2 * x1, K / (2 * x2))
Then we use the point-to-point distance formula to get the polynomial made of Mn = K and x1
Another equation with K and X1 is obtained by using the slope of the line where Mn is located as - 1 / root 3
To sum up, two unknowns and two equations can solve the value of K
2 radical 3