find the path of a moving point such its distance is from two lines 3x-2y=5and 3x+2y=5 are equal and state the name of path.

The two given line are 

3x-2y=5 .........(i)

3x+2y=5 .........(ii)

Let (h,k ) is any point whose distances from the lines (i) and (ii), are equal.

Thus, the point (h,k) satisfies the equation y = 0 and x = 5/3, which represents  straight  lines.  

Hence, path of the point equidistant from the lines (i) and (ii) is a straight line.