# 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 