As shown in Figure 4, cross a focal point (- 1,0) of the ellipse x ^ 2 + 2Y ^ 2 = 2 to make a straight line intersection ellipse a, two points o of B as the origin of the coordinates. Find the maximum area of the triangle AOB

1、 Let x = - 1 in x ^ 2 + 2Y ^ 2 = 2, we get: 1 + 2Y ^ 2 = 2, y ^ 2 = 1 / 2, y = 2 / 2, or y = - 2 / 2. In this case, ab = 2. Obviously, the distance from point o to ab = 1

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