将y=kx+2代入x²=4y,得 x²-4kx-8=0,
x1+x2=4k,x1x2=-8
y1+y2=(kx1+2)+(kx2+2)=k(x1+x2)+4=4k²+4
(1)当k=2时,x1+x2=8,x1x2=-8
(x2-x1)²=(x1+x2)² -4x1x2=64+32=96,|x2-x1|=4√6
|AB|=[√(1+k²)]•|x2-x1|=4√30
(2) |OA+OB|²=(x1+x2)²+(y1+y2)²=16k²+16(k²+1)²
从而 k=0时,有最小值 |OA+OB|²=16,|OA+OB|=4