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Question

Find the equation of the line mid - way between the parallel lines 9x+6y7=0 and 3x+2y+6=0.


Solution

The equation of lines are

3x+2y73=0(i)

3x+2y+6=0(ii)

Let equation of mid way be

3x+2y+λ=0(iii)

Then, distance between (i) and (iii) and (ii) and (iii) should be equal.

λ+739+4

λ+73=π+6

λ=116

The required line is 3x+2y+116=0 or 18x+12y+11=0

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