Question

If 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.

Answer 1

The equations of the given lines are x 

+ y – 5 = 0 … (1)
3x – 2y + 7 = 0 … (2)
The perpendicular distances of P (x, y) from lines (1) and (2) are respectively given by

which is the equation of a line.
Similarly, we can obtain the equation of line for any signs of  (X +Y - 5) and (3x -2y + 7)
Thus, point P must move on a line.