Question

the dustance between the parallel lines y=2x+4and 6x=3y+5 is )17/root3 b) 1 c) 3/root 5 d) 17root5/15 please help me it's urgent

Answer 1

the correct option is d) 17root5/15
GIVEN
y=2x+4
6x=3y+5

solution,
2x-y+4=0
6x-3y-5=0
÷ by 3
2x-y-5/3=0
THE DISTANCE BETWEEN THE PARALLEL LINES IS
C1 - C2 /root of a square + b square

here
a=2. b= -1. C1=4. C2= -5/3

= 4+5/3÷root 2 square +(-1)square

= 12+5/3÷root 5
=17/3×root 5
= 17×root 5 / 3 root 5× root 5
= 17×root 5 / 3×5

= 17×root 5/15
That the answer is came.