gaokao 2015 Q19

gaokao · China · zhejiang-science Circles Area and Geometric Measurement Involving Circles
19. (This question is worth 15 points) Two distinct points $A , B$ on the ellipse $\frac { x ^ { 2 } } { 2 } + y ^ { 2 } = 1$ are symmetric about the line $y = mx + \frac { 1 } { 2 }$ . (I) Find the range of the real number $m$; (II) Find the maximum value of the area of $\triangle AOB$ (where $O$ is the origin). [Figure]
19. (This question is worth 15 points)\\
Two distinct points $A , B$ on the ellipse $\frac { x ^ { 2 } } { 2 } + y ^ { 2 } = 1$ are symmetric about the line $y = mx + \frac { 1 } { 2 }$ .\\
(I) Find the range of the real number $m$;\\
(II) Find the maximum value of the area of $\triangle AOB$ (where $O$ is the origin).\\
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