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

The equations of the given lines are

9x + 6y – 7 = 0 ---------------- (1)

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

Let P (h, k) be the arbitrary point that is equidistant from (1) and (2).

The perpendicular distance of P(h, k) from line (1) is given by

The perpendicular distance of P(h, k) from line (2) is given by

Since, P (h, k) is equidistant from lines (1) and (2),

Thus,

or

So, when is not possible as

which is not at all possible

And when

9h + 6k – 7 = -9h – 6k – 18

18h + 12k +11 = 0

Therefore, the required equation of the line is 18h + 12k +11 = 0.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1169 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses