If F1 and F2 are the focus of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, and P is the point on the ellipse that is not on the X axis, then the trajectory equation of the center of gravity g of △ pf1f2 is
F1(-3,0),F2(3,0).
Let g (x, y) P (x0, Y0)
x=x0/3
y=y0/3
Then x0 = 3x, Y0 = 3Y
Because point P is on the ellipse, then x0 ^ 2 / 25 + Y0 ^ 2 / 16 = 1
So 9x ^ 2 / 25 + 9y ^ 2 / 16 = 1,
Point P is not on the X axis, so Y0 ≠ 0, then y ≠ 0
The trajectory equation is 9x ^ 2 / 25 + 9y ^ 2 / 16 = 1 (Y ≠ 0)
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