Prove that the locus of a moving point, which is equidistant from the lines `3x-2y=5` and `3x+2y=5`, is a straight line.

Explanation

Let the point be `(x,y)` then
`|(3x-2y-5)/(sqrt(9+4))|=|(3x+2y-5)/(sqrt(9+4))|`
`implies |3x-2y-5|=|3x+2y-5|`
`implies(3x-2y-5)=+-(3x+2y-5)`
`implies3x-2y-5=3x+2y-5`
or `3x-2y-5=-(3x+2y-5)`
`implies x=(5)/(3)` or `y=0`
Which are the equations of straight lines.
Therefore, the required locus is a straight line.