amaths

For a),
Sub y=0 into L1,
2x-3(0)-2=0
2x-0-2=0
2x-2=0
2x=2
x=1 (proved)

For b),
Since they are parallel,something like this shape / / , they both touches the x-axis.
The picture
/ /
/ /
/ /
------------/------------/-------------> x
Use the two points touching the x-axis. (x1,0) and (x2,0).
You should know how to find x1 and x2.
After finding x1 and x2, use the formula length= square root[(x1-x2)+(y1-y2)].
This is the final answer.

(a) 2(1) - 3(0) - 2 = 2-2 = 0
Hence (1, 0) lies on L1
(b) Since the two lines are parallel, distance between two lines equal to the distance between (1,0) and L2.
Distance required =|[4(1) - 6(0) - 5]/sqrt(4^2 + 6^2)|
= |-1/sqrt(52)|
= 1/2sqrt(13)
= sqrt(13)/26