Question

Find K so that the line L1 =(2-k)x-y =-1 and L2=8x+ky=12 find

a) parallel to each other
b) perpendicular to each othetr

Answer 1

Step-by-step explanation:

(m1) slope of L1=-(2-k)/-1=2-k

(m2) slope of L2=-8/k

a)

if they are parallel

m1=m2

2-k=-8/k

2k-k²=-8

k²-2k-8=0

k²-4k+2k-8=0

k(k-4)+2(k-4)=0

(k-4)(k+2)=0

either

k=4

or

k=-2

when lines are perpendicular

m1m2=-1

(2-k)×-8/k=-1

-16+8k=-k

8k+k=16

9k=16

k=16/9