It is known that P is a point on the hyperbola X / 16-y / 9 = 1 with F1 and F2 as the focus, and the trajectory equation of the center of gravity g of △ f1f2p is obtained RT

It is known that P is a point on the hyperbola X / 16-y / 9 = 1 with F1 and F2 as the focus, and the trajectory equation of the center of gravity g of △ f1f2p is obtained RT

First of all, the center of gravity g should be the intersection of the three midlines of △ f1f2p (the center of gravity is 1:2, that is, one of the three equal points is close to the bottom), so if the origin coordinate o is set, the center of gravity must be on OP, and og: GP = 1:2
So let P coordinate X, y, then OP vector (x, y) vector og: OP = 1:3, so let g coordinate (x, y)
Then x = 3x, y = 3Y, P brings X and Y into the hyperbola and arranges them into 9x ^ 2-16y ^ 2 = 16