This is the Important question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD.
Two parallel lines are given, So find the relation connecting a and b.
This is the Question Number 03, Exercise 12.2 of M.L Aggarwal.
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Lines 2x – by + 5 = 0 and ax + 3y = 2 are parallel. Find the relation connecting a and b.
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Given lines are: 2x – by + 5 = 0 and ax + 3y = 2
If two lines to be parallel then their slopes must be equal.
In equation 2x – by + 5 = 0,
by = 2x + 5
y = (2/b) x + 5/b
So, the slope of the line (m1) = 2/b
And in equation ax + 3y = 2,
3y = -ax + 2
y = (-a/3) x + 2/3
So, the slope of the line (m2) = (-a/3)
As the lines are parallel
m1 = m2
2/b = -a/3
6 = -ab
Hence, the relation connecting a and b is ab + 6 = 0