Let ABCD be a rectangle with $A(0, 0), B(4, 0), C(4, 4) and D(0, 4)$. Rectangle is folded in such a way that corner B always lies on line AD, then which of the following statement(s) is/are CORRECT?

As the point B moves on AD the crease thus formed will touch a fixed parabola whose focus is at (4, 0).

As the point B moves on AD the crease thus formed will touch a fixed parabola whose equation of directrix is $y = 2x.$

As the point B moves on AD the crease thus formed will touch a fixed parabola whose focus is at  $(\frac{3}{2},0)$.

As the point B moves on AD the crease thus formed will touch a fixed parabola whose equation is  $y^2=8(x-2)$.