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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.