It is known that a straight line y = (K1-1) x + 2 and a hyperbola y = K2 / X intersect at two points a (2,4) and B. (1) find the coordinates of point B. (2) find the area of triangle AOB Please chop the proof of s △ AOB into Connect OA, ob

It is known that a straight line y = (K1-1) x + 2 and a hyperbola y = K2 / X intersect at two points a (2,4) and B. (1) find the coordinates of point B. (2) find the area of triangle AOB Please chop the proof of s △ AOB into Connect OA, ob

The area of b-coordinate (- 4, - 2) is 2
According to point a (2,4), K1 = 3, K2 = 8 are calculated
So: y = 3x + 2, y = 8 / X
So the coordinate of the x-axis at the intersection of the line y = 3x + 2 is - 2 / 3
The triangle ABO is divided into two parts
2 / 3 at the bottom
Above X-axis: 1 / 2 * 2 / 3 * 4 = 4 / 3
Below the x-axis: 1 / 2 * 2 / 3 * 2 = 2 / 3
The total is 2

In the plane rectangular coordinate system, the line y = K1X and hyperbola y = K2 / X intersect at point a (- 2,3) B, then the coordinates of point B are

3 = K1 × (- 2), 3 = K2 / (- 2)
The solution is K1 = - 3 / 2, K2 = - 6
So the straight line y = - 3 / 2x, the hyperbola y = - 6 / X
If y = - 3 / 2x, y = - 6 / x, the solution is x = 2, y = - 3 or x = - 2, y = 3
So B (2, - 3)

The straight line Y1 = K1X (K1 > 0) and the straight line y2 = k2x (K2 > 0) intersect the hyperbola y = K / X (k > 0) at points a, B and C, D, respectively

Both positive and negative scaling functions are symmetric about the origin
So intersection a and B are symmetric at the origin
Then o is the midpoint of ab
Similarly, O is the midpoint of CD
AB and CD are diagonals of quadrilateral
That is, the diagonals are equally divided
So it's a parallelogram

In RT △ ABC, ∠ C = 90 °, a = 60 ° and BC = 6, equilateral △ def moves from the initial position (point e coincides with point B, EF falls on BC, as shown in Figure 1) along the BC direction at a speed of 1 unit per second, de and DF intersect AB at points m and N respectively. When point F moves to point C, △ def stops moving, and point d just falls on ab
Q: a few seconds after the start of the movement, point m is just the midpoint of de

Angle a is 60 degrees, when point F moves to C, point D of triangle def just falls on AB, then the side length of triangle DEF is 3, and the length from m to e is 1.5