The locus of the midpoints of the chords of an ellipse `x^(2) + 4y^(2) = 4 ` that are drawn forms the positive end of the minor axis is

Options

A. a circle with centre `((1)/(2),0)`, and radius 1
B. a parabola with focus `((1)/(2),0)`, and directrix x = - 1
C. an ellipse with centre `(0,(1)/(2))` , major axis 1 and minor axis `(1)/(2)`
D. a hyperbola with centre `(0,(1)/(2))` , transverse axis 1 and conjugate axis `(1)/(2)`