Question

Which of the following is wrong statements.

a) a1x+ b1y + c1 = 0 and a2x + b2y + c2 = 0 two straight lines ie 1

2

=

1

2

two lines

are parallel.​

Answer 1

Answer: hey there,

Step-by-step explanation: When two lines are parallel, both are either vertical or non-vertical. If both are vertical, then b1 = b2 = 0 so that a1b2 = a2b1 = 0. If both are non-vertical, their slopes are equal. Thus  - a1/b1 = -a2/b2 Hence,   a1b2 = a2b1  or  a1:b1 = a2:b2  Conversely, when a1b2 = a2b1 and if b1 = 0, then a1 ≠ 0 so that b2 = 0. Therefore, b1 = 0 ⇔ b2 = 0 and hence if one of the lines is vertical, then the other is also vertical so that the given lines are parallel. If both b1 and b2 are non-zero, then

Since the slopes are equal, the lines are parallel.