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.

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|/sqrt(3^2+2^2) = |3h + 2k – 5| /sqrt(3^2+5^2)`

=`|3h – 2k – 5|=|3h + 2k – 5|`

⇒ `3h – 2k – 5 = pm(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.