已知直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0.

问题描述:

已知直线L1:5x-2y+3m(3m+1)=0与L2:2x+6y-3m(9m+20)=0.
当m为何值时,两直线的交点到直线4x-3y-12=0的距离最小?最小值为多少?

5x-2y+3m(3m+1)=0(1)2x+6y-3m(9m+20)=0(2)(1)×3+(2)17x+9m(3m+1)-3m(9m+20)=017x=27m²+60m-27m²-9m17x=51mx=3m代入(2)6m+6y=3m(9m+20)m+y=m(9m+20)/2y=(9m²+18m)/2到直线距离d=|12m-3/2(9m²...