Q. 214.3( 25 Votes )
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
Answer :
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.
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PREVIOUSIf sum of the perpendicular distances of a variable point P (x, y) from the lines x + y – 5 = 0 and 3x – 2y +7 = 0 is always 10. Show that P must move on a line.NEXTA ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
