Q. 55.0( 2 Votes )

Find the equation of the line mid-way between the parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.

Answer :

Given:


9x + 6y – 7 = 0 and 3x + 2y + 6 = 0 are parallel lines


To find:


The equation of the line mid-way between the givens line


Explanation:


The given equations of the lines can be written as:


… (1)


3x + 2y + 6 = 0 … (2)


Let the equation of the line midway between the parallel lines (1) and (2) be


3x + 2y + λ = 0 … (3)


The distance between (1) and (3) and the distance between (2) and (3) are equal.






Equation of the required line:



18x + 12y + 11 = 0


Hence, equation of required line is 18x + 12y + 11 = 0.


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