y2=16x is a parabola and x2+y2=16 is a circle . Then
circle passes through the vertex of the parabola
circle touches the parabola at the vertex
circle passes through the focus of the parabola
circle lies inside the parabola.
Centre of the circle is the origin, the vertex of the parabola and the focus of the parabola is A (4, 0). The circle passes through A.