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Find equation of the line which is eq...

Find equation of the line which is equidistant from parallel lines `9x" "+" "6y" "" "7" "=" "0` and `3x" "+" "2y" "+6" "=" "0` .

Text Solution

Verified by Experts

The equations of the given lines are
`9x+6y-7=0 " " (1)`
and 3x+2y+6=0
`or 9x+6y+18=0 " " (2)`
The line parallel to the above lines is
`9x+6y+c=0 " " (3)`
The distance of line (3) from lines (1) and (2) is the same.
Therefore,
`(|C-18|)/(sqrt(9^(2)+6^(2))) = (|C+7|)/(sqrt(9^(2)+6^(2)))`
or c-18 = -c-7
`c=(11)/(2)`
Therefore, the equation of the line is 18x + 12y + 11 =0.
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