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.