It is known that the line L: y = K (x + 2 √ 2) and the circle O: x ^ 2 + y ^ 2 = 4 intersect at two points a and B. o is the origin of the coordinate and the area of the triangle abo It is known that the line L: y = K (x + 2 √ 2) and the circle O: x ^ 2 + y ^ 2 = 4 intersect at two points a and B, O is the origin of the coordinate, and the area of the triangle ABO is s ① Try to express s as a function s (k) and find its domain of definition ② Find the maximum value of S and the value of K when the maximum value is obtained

It is known that the line L: y = K (x + 2 √ 2) and the circle O: x ^ 2 + y ^ 2 = 4 intersect at two points a and B. o is the origin of the coordinate and the area of the triangle abo It is known that the line L: y = K (x + 2 √ 2) and the circle O: x ^ 2 + y ^ 2 = 4 intersect at two points a and B, O is the origin of the coordinate, and the area of the triangle ABO is s ① Try to express s as a function s (k) and find its domain of definition ② Find the maximum value of S and the value of K when the maximum value is obtained

It's a little troublesome. In fact, it's very simple. I know the distance from the origin to the straight line. Then I combine the two equations to find the coordinates of the two intersecting points. I know the distance between the two points, and then I know the surface level of the triangle
The domain of definition is that the line must pass the point (- 2 √ 2.0), and then there are two points on the circle that have only one intersection with the circle
In between is the domain
The maximum value is zero. It is solvable. This is inconvenient