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例直线l:y=-1/2x+2与椭圆(x2)/(a2)+(y2)/(b2)=1交于A、B两点,O为坐标原点,M为线段AB的中点.若|AB|=5~(1/2),直线OM的斜率为1/2,求椭圆的方程.
The straight line l:y=-1/2x+2 and ellipse(x2)/(a2)+(y2)/(b2)=1 are intersected at two points A and B. O is the origin of coordinates, and M is the middle of line AB. If |AB|=5~(1/2), the slope of the straight line OM is 1/2, find the equation of the ellipse.