The locus of the mid-point of the line segment joining the focus of the parabola to a moving point of the parabola is another parabola whose directrix is:
Explanation of the correct option.
Compute the directrix:
Given :
Let's plot the graph.
Let is the midpoint of the line segment.
From the graph,
…………….
Substitute the value of in equation ,
Locus of is
Therefore its directrix is
Hence, option is the correct answer.