The locus of the midpoint of the chord of the circle which makes an angle of at the center, is
Explanation of the correct option.
Compute the locus:
Given :
It is a circle with a radius of and center at .
Let the midpoint of the chord is .
Let's plot the figure.
From the figure,
Since
From the distance formula,
Therefore, the locus of is
Hence, option is the correct answer.