1.设直线l方程为y=kx+3,A(a1,b1),B(a2,b2)
联立抛物线方程x^2=2y,消去y,得到x^2=2(kx+3)
整理得：x^2-2kx-6=0
a1+a2=2k,a1*a2=-6
向量OA*向量Ob
=a1*a2+b1*b2
=a1*a2+(ka1+3)(ka2+3)
=(k^2+1)a1*a2+3k(a1+a2)+9=(k^2+1)(-6)+3k*2k+9=3
得证!
2.设过P的直线方程为y=k(x-1)
联立x^2=2y,消去y,得到x^2=2k(x-1)
整理得：x^2-2kx+2k=0
（-2k)^2-4*2k=0
求得k=0,2
所以切线方程为y=0,y=2(x-1)