4. If a circle with a diameter defined by a chord passing through a focus of a conic section has no common points with the corresponding directrix, then the conic section is ( ).
(A) Hyperbola
(B) Ellipse
(C) Parabola
(D) Ellipse or Hyperbola
4.B.

As shown in Figure 7, F is the focus, and the corresponding directrix is $l$. AB is the focal chord, M is the midpoint of AB, and the projections of A, M, B on $l$ are G, N, H, respectively. Let $e$ be its eccentricity. According to the definition of conic sections, we have
$$
\begin{aligned}
A F & =e \cdot A G, \\
B F & =e \cdot B H .
\end{aligned}
$$

Therefore, $A B=e(A G+B H)=2 e \cdot M N$, so $e=\frac{A B}{2 M N}$. Since the circle with AB as its diameter is separated from $l$, it follows that $e=\frac{A B}{2 M N}<1$.