Through the right focus F of hyperbola C: x2-y23 = 1, make a straight line L intersecting hyperbola C at P and Q, OM = OP + OQ, then the trajectory equation of point m is______ ．

Through the right focus F of hyperbola C: x2-y23 = 1, make a straight line L intersecting hyperbola C at P and Q, OM = OP + OQ, then the trajectory equation of point m is______ ．

Let the linear equation: KY = X-2 & nbsp; & nbsp; solve the simultaneous equations: (3k2-1) Y2 + 12ky + 9 = 0, let P (x1, Y1) & nbsp; Q (X2, Y2) & nbsp; m (x, y) mean: x = X1 + x2 & nbsp; & nbsp; & nbsp; & nbsp; y = Y1 + Y2, so x = - 23k2 − 1 & nbsp; y = -- 12k3k2 − 1 & nbsp; & nbsp; eliminate K to get: (x-1) 2-y212 = 1, so the trajectory equation of point m: (x-1) 2-y212 = 1, so the answer is: (x-1) 2-y212 = 1