Given the hyperbola x ^ 2-y ^ 2 / 2 = 1, the line L passing through point a (2,1) intersects with the given hyperbola at two points P1 and P2, and the trajectory equation of point P in line p1p2 is obtained

Given the hyperbola x ^ 2-y ^ 2 / 2 = 1, the line L passing through point a (2,1) intersects with the given hyperbola at two points P1 and P2, and the trajectory equation of point P in line p1p2 is obtained

Let the linear equation be Y-1 = K (X-2), P1 and P2 be (x1, Y1), (X2, Y2), and the midpoint coordinate be ((x1 + x2) / 2, (Y1 + Y2) / 2). Substitute the coordinates of two points into the equation respectively, and then subtract the two equations to get: (x1-x2) * (x1 + x2) = 0.5 * (y1-y2) * (Y1 + Y2) (y1-y2) / (x1-x2) = 2 * (x1 + x2) / (Y1 + Y2)