1)拋物線的焦點為（1,0）,y=k(x-1),帶入k^2(x-1)^2=4x,整理得x^2-(2+4/k^2)+1=0,根據(jù)根與系數(shù)的關(guān)系,x1*x2=1；x1+x2=2+4/k^2；y1*y2=k^2(x1-1)(x2-1)=k^2(x1*x2-x1-x2+1)=-4,所以O(shè)A*OB=-3
2)令直線L: y=kx+b,帶入拋物線方程(kx+b)^2=4x,整理得x^2-((4-2kb)/k^2)x+b^2/k^2=0;
根據(jù)根與系數(shù)的關(guān)系,x1*x2=b^2/k^2,x1+x2=(4-2kb)/k^2；y1*y2=(kx1+b)(kx2+b)=k^2x1*x2+kb(x1+x2)+b^2=b^2+(4-2kb)*kb/k^2+b^2=4kb/K^2；所以x1x2+y1y2=(b^2+4kb)/k^2=-4；整理的(2k+b)2=0；即2k+b=0；b=-2k；所以L：y=k(x-2),這條直線過點(2,0)