Question

已知平行直线l1与l2的距离为根号5,且直线l1经过原点,直线l2经过点(1,3),求直线l1和直线l2的方程

Answer 1

设二直线的斜率是k

则有:

L1:y=kx

L2:y=k(x-1)+3,即kx-y-k+3=0

d=|-k+3|/根号(1+k^2)=根号5

(k-3)^2=5(1+k^2)

k^2-6k+9=5+5k^2

4k^2+6k-4=0

2k^2+3k-2=0

(2k-1)(k+2)=0

k1=1/2

k2=-2

即方程是:

L1:y=1/2x或y=-2x

L2:y=x/2+5/2或y=-2x+5