Zhejiang 20 1 1 Mathematical Analytic Geometry of College Entrance Examination. Why did k 1+k2 k 1k2 get the latter formula?

In the reference answers given on the following pages.

/view/a2e 447 a6b 07 17fd 5360 CDC 27 . html

With x0 said k 1+k2 and k 1*k2, the solution idea:

(1) First, find the abscissa of A and B.

Y = kx-kx0+x0 2, y = x 2, elimination and simplification of y.

x^2-kx+kx0-x0^2=0

Because x0 must be its root, and the product of two roots is kx0-x0 2, and the other root is k-x0.

When k=k 1, the abscissa of a is x 1=k 1-x0.

When k=k2, the abscissa of b is x 1=k2-x0.

(2) calculate the slope of line AB: k (ab) = (x12-x22)/(x1-x2) = x1+x2 = k1+k2-2x0 = ...

Calculate the slope of MP straight line: k (MP) = (x0 2-4)/x0.

(3) Solve the vertical relation equation to get x0, and finally get the result.

I hope I can help you!