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In △ ABC, a > b > C, and C = (a + b) / 2, if vertex a (- 1,0), B (1,0), find the trajectory equation of vertex C
From C = (a + b) / 2, a + B = 2C = 2 ab = 2 1 - (- 1) = 4 = constant,
That is: the sum of distances from point C to points a and B is constant, and the locus of point C is ellipse
From a + B = 4, we can see that the major half axis of the ellipse is 2. From a (- 1,0) and B (1,0), we can see that the focus a and B of the ellipse are on the x-axis
The focal length is ab = 2, the short half axis is √ (2 ^ 2-1 ^ 2) = √ 3
The trajectory equation of C is: x ^ 2 / 4 + y ^ 2 / 3 = 1
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