Let f be the focus of the parabola y2 = 4x, and a, B, C be the three points on the parabola. If the center of gravity of the points a (1,2), △ ABC coincides with the focus F of the parabola, Then the equation of the line where the BC edge is located is

Let f be the focus of the parabola y2 = 4x, and a, B, C be the three points on the parabola. If the center of gravity of the points a (1,2), △ ABC coincides with the focus F of the parabola, Then the equation of the line where the BC edge is located is

Let B (x1, Y1) C (X2, Y2), let D (x0, Y0) in BC have x0 = (x1 + x1) / 2, Y0 = (Y1 + Y2) / 2, because the center of gravity of △ ABC coincides with the focus F of the parabola, so the center f (1,0) is 1 = (x1 + x2 + 1) / 30 = (Y1 + Y2 + 2) / 3 to get X1 + x2 = 2, Y1 + y2 = - 2, so D (1, - 1) takes B C into the parabola equation to get