It is known that the square of the line passing through the parabola y is equal to the focus F of 4x, and intersects with the parabola at two points a and B The first question is to find the area of the triangle ABO when the oblique line is 1. The second question is to find the trajectory equation of the midpoint m of the focus chord ab

It is known that the square of the line passing through the parabola y is equal to the focus F of 4x, and intersects with the parabola at two points a and B The first question is to find the area of the triangle ABO when the oblique line is 1. The second question is to find the trajectory equation of the midpoint m of the focus chord ab

Focus f (1,0) AB: y = X-1, y ^ 2 = 4 (y + 1) Y1 = 2 + 2 radical 2, y2 = 2-2 radical 2S (OAB) = 1 / 2of (y1-y2) = 1 / 2 * 1 * 4 radical 2 = 2 radical 2 let the line be y = K (x-1) k ^ 2 (x ^ 2-2x + 1) = 4xk ^ 2x ^ 2 - (2k ^ 2 + 4) x + K ^ 2 = 0x1 + x2 = (2k ^ 2 + 4) / K ^ 2 = 2 + 4 / K ^ 2