Correct Answer: Option D

Explanation

The set of points equidistant from two parallel lines can be determined by the perpendicular distance from a point to each line.

Given the lines are of the form ax + by + k\(_1\) = 0 and ax + by + k\(_2\) = 0, the locus of points equidistant from these lines is another line parallel to them.

To find this line, which represents the equation of the locus, we need to find the average  k\(_1\) and  k\(_2\), which we shall be denoted by q

This line will have the same coefficients for x and y as the original lines.

Thus, the equation of the locus is: ax + by + q = 0

There is an explanation video available below.

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