There is a moving point P on the ellipse X / 9 + y2 = 1. F1 and F2 are the two focal points of the ellipse. The trajectory equation of the center of gravity m of △ pf1f2 is obtained

There is a moving point P on the ellipse X / 9 + y2 = 1. F1 and F2 are the two focal points of the ellipse. The trajectory equation of the center of gravity m of △ pf1f2 is obtained

Let m (x, y), P (x ', y')
From the ellipse X / 9 + y2 = 1
Know C ^ 2 = 9-1 = 8
That is, C = 2 √ 2
So F1 (2 √ 2,0) F2 (- 2 √ 2,0) P (x ', y')
M is the center of gravity of △ pf1f2
Then x = (x '+ 2 √ 2-2 √ 2) / 3
y=(y'+0-0)/3
That is to say, X '= 3x
y'=3y
From P (x ', y') in
On the ellipse x ^ 2 / 9 + y2 = 1
Then x '^ 2 / 9 + y'2 = 1
So (3x) ^ 2 / 9 + (3Y) 2 = 1
so
Trajectory equation of center of gravity m of △ pf1f2
X ^ 2 + y 2 / (1 / 9) = 1 (Y ≠ 0)