Let the distance between the parabola y = x ^ 2 + ax + A-2 and the two intersections of X axis be 2, then the value of a is?

Let the distance between the parabola y = x ^ 2 + ax + A-2 and the two intersections of X axis be 2, then the value of a is?

The transformation of geometric language into algebraic language is "the difference between two solutions of x ^ 2 + ax + A-2 = 0 is 2."
That is, x1-x2 = 2, and from WIDA's theorem, we get X1 + x2 = - A, x1x2 = A-2
We can get 4x1x2 = (x1 + x2) ^ 2 - (x1-x2) ^ 2 = a ^ 2-4 = 4 (A-2)
(a+2)(a-2)-4(a-2)=0,(a-2)^2=0,a=2

The coordinates of the shortest point on the parabola y = X2 to the line 2x-y-4 = 0 are ()
A. （1，1）B. （12，14）C. (32，94)D. （2，4）

Let a point on the parabola y = x2 be a (x0, X02), and the distance d from point a (x0, X02) to the straight line 2x-y-4 = 0 = | 2x0 − X02 − 4 | 4 + 1 = 55 | (x0 − 1) 2 + 3 |. When x0 = 1, that is, when a (1, 1), the distance from a point on the parabola y = X2 to the straight line 2x-y-4 = 0 is the shortest

The coordinates of the shortest point on the parabola y = X2 to the line 2x-y-4 = 0 are ()
A. （1，1）B. （12，14）C. (32，94)D. （2，4）

Let a point on the parabola y = x2 be a (x0, X02), and the distance d from point a (x0, X02) to the straight line 2x-y-4 = 0 = | 2x0 − X02 − 4 | 4 + 1 = 55 | (x0 − 1) 2 + 3 |. When x0 = 1, that is, when a (1, 1), the distance from a point on the parabola y = X2 to the straight line 2x-y-4 = 0 is the shortest

The coordinates of the point with the shortest distance from the parabola y2 = 2x to the point P line X-Y + 3 = 0 are___ ．

Let this point be p. if the ordinate is a, then A2 = 2x, so the distance from P (A22, a) P to x + y + 3 = 0, d = | A22 + A + 3 | 1 + 1 ∵ A22 + A + 3 = 12 (a + 1) 2 + 52, so when a = - 1, A22 + A + 3 is the smallest, so p (12, - 1)