6. If the parabola satisfies the following conditions:
(1) the directrix is the $y$-axis;
(2) the vertex is on the $x$-axis;
(3) the minimum distance from point $A(3,0)$ to a moving point $P$ on the parabola is 2.
Then the number of such parabolas is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
6.D.

Suppose there exists such a parabola, with vertex $B$ on the $x$-axis. Let $B(a, 0)$, then the equation of the parabola with the $y$-axis as the directrix is
$$
y^{2}=4 a(x-a) \text {. }
$$

From condition (3), we know that $a>0$. Let $P\left(\frac{m^{2}}{4 a}+a, m\right)$, thus,
$$
\begin{array}{l}
|A P|^{2}=\left(\frac{m^{2}}{4 a}+a-3\right)^{2}+m^{2} \\
=\frac{1}{16 a^{2}}\left[m^{2}-12\left(a-a^{2}\right)\right]^{2}+12 a-8 a^{2} .
\end{array}
$$

When $a-a^{2} \geqslant 0$, i.e., $01$, by setting $m=0$ we get
$$
|A P|_{\text {min }}=|a-3|=2 \text {. }
$$

Solving this gives $a=5$.
The equation of the parabola is $y^{2}=20(x-5)$.
Therefore, there are 3 parabolas that satisfy the conditions.