Question

Show that the path of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line.

Answer 1

Given:

Two lines 3x – 2y = 5 and 3x + 2y = 5 

To prove: 

The path of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line 

Concept Used: 

Distance of a point from a line. 

Explanation:

 

Let P(h, k) be the moving point such that it is equidistant from the lines 3x − 2y = 5 and 3x + 2y = 5

⇒ |3h – 2k – 5| = |3h + 2k – 5| 

⇒ 3h – 2k – 5 = ±(3h + 2k – 5) 

⇒ 3h – 2k – 5 = 3h + 2k – 5 and 3h – 2k – 5 = -3h + 2k – 5

⇒ k = 0 and 3h = 5 

Hence proved, the path of the moving points are 3x = 5 or y = 0. These are straight lines.