20 14 Beijing senior high school entrance examination explains mathematics

1 solution: let the parabolic equation be: y = ax 2+bx+c;

Because about y symmetry, B = 0, y = y = ax 2+c;

x=0，c=，x=-2，y=0，

The solution is a=-sqrt(3)/2.

y=( 1-x^2/4)

2 solution: Because OC=, AO=2, so

A triangle with vertices A, P and Q is similar to △AOC and needs AP= 1/2QA.

So t= 1/2(4-2t).

So t= 1

3 solution: minimize AM+MN+NP, NP must be perpendicular to AC, MB must be connected, so BM must be perpendicular to AC.

BM=4sqrt(3)/3，m=MO=/3，AM+MN+NP=+ 1/2，t=2+sqrt(3)/2