Question

The 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

Given lines are 

x + y – 5 – 0 ………. (1) 

3x – 2y + 7 = 0  …………. (2) 

Also, 

Distance of (1) from P + distance of (2) from R = 10

Which gives a set of four lines.

⇒ P must move on any one of the four lines.