In the rectangular coordinate system as shown in the figure, a and B are two points on the x-axis, and the circle with ab as the diameter intersects the y-axis at C. suppose that the analytical formula of the parabola passing through a, B and C is y = xx-mx + N, and the sum of the two reciprocal of the equation xx-mx + n = 0 is - 2 (1) Find the value of n (2) Find the analytical formula of this parabola (3) Let a straight line parallel to the x-axis intersect the parabola at two points E and F. ask if there is a circle with the diameter of line segments E and f just tangent to the x-axis? If so, find out the radius of the circle; if not, explain the reason

In the rectangular coordinate system as shown in the figure, a and B are two points on the x-axis, and the circle with ab as the diameter intersects the y-axis at C. suppose that the analytical formula of the parabola passing through a, B and C is y = xx-mx + N, and the sum of the two reciprocal of the equation xx-mx + n = 0 is - 2 (1) Find the value of n (2) Find the analytical formula of this parabola (3) Let a straight line parallel to the x-axis intersect the parabola at two points E and F. ask if there is a circle with the diameter of line segments E and f just tangent to the x-axis? If so, find out the radius of the circle; if not, explain the reason

(1) Let a (a, 0), B (B, 0) and a circle B intersect Y axis, so a and B are positive and negative
Because the parabola passing through a, B, C is y = xx-mx + N, so C (0, n) n is not equal to 0
AB is the diameter, then the triangle ABC is a right triangle, the angle c is a right angle, and CO is perpendicular to AB, so the square of CO = AO * Bo
That is NN = | ab | = - N,
N = - 1
(2) The sum of the two reciprocal of equation xx-mx + n = 0 is - 2
That is, 1 / A + 1 / b = (a + b) / AB = m / N = - 2, M = 2
The analytical expression of parabola is
Y=XX-2X-1
(3) The axis of symmetry of the parabola is x = 1
So we can assume that the center of the circle EF is d (1, d)
E（e,d）,F（f,d）
Suppose there is such a circle tangent to the X axis, then EF = | F-E | = 2 | D|
Substituting E and f into parabola
ee-2e-1=d
ff-2f-1=d
Let | F-E | = 2 | D | be squared to ff-2fe + EE = (F + e) * (F + e) - 4Fe = 4dd
f. E is the solution of the equation xx-2x-1-d = 0, so
（f+e）*（f+e）-4fe=2*2-4*（-1-d）=8+4d=4dd,
The results show that dd-d-2 = 0, d = 2 or D = - 1, and D is in the effective interval of parabola
So there are two circles