Let \( A \) be a fixed point \( (0, 6) \) and \( B \) be a moving point \( (2t, 0) \). Let \( M \) be the mid-point of \( AB \) and the perpendicular bisector of \( AB \) meets the \( y \)-axis at \( C \). The locus of the mid-point \( P \) of \( MC \) is:
