The end points a and B of the line segment AB of fixed length four move on the parabola X & # 178; = y, and the line where AB is located passes the focus. The minimum distance from the midpoint C of AB to the X axis is obtained, And find the coordinates of point C in AB at this time

The end points a and B of the line segment AB of fixed length four move on the parabola X & # 178; = y, and the line where AB is located passes the focus. The minimum distance from the midpoint C of AB to the X axis is obtained, And find the coordinates of point C in AB at this time

7 / 4 (± SQR (3) / 2,7 / 4) let the straight line AB be y = KX + B, a (m, P), B (n, q); and y = x ^ 2-kx-b = 0. From the relationship between the root and coefficient of the quadratic equation of one variable: M + n = Kmn = - B ∵ AB length is 4, | ab | ^ 2 = 16 (m-n) ^ 2 + (P-Q) ^ 2 = (m-n) ^ 2 + K ^ 2 * (m-n) ^ 2 = (m-n) ^ 2 * (1 + K ^ 2) = [(M + n) ^ 2]