5 In the circle $\odot O$ with radius 1, take a fixed point $A$ and a moving point $B$. Let point $P$ satisfy $A P / / O B$ and $\overrightarrow{A P} \cdot \overrightarrow{A B}=1$, then the trajectory of point $P$ is ( ).
(A) Ellipse
(B) Parabola
(C) Hyperbola
(D) Any of the above is possible
5 $\mathrm{B}$ Hint: Let $O(0,0), A(1,0), P(x, y)$. Since $A P / /$ $O B$, we can set $B(k(x-1), k y)$. Substituting these coordinates into $\overrightarrow{A P} \cdot \overrightarrow{A B}=1$. We get $k=$ $\frac{x}{(x-1)^{2}+y^{2}}$. Finally, using that $B$ is on $\odot O$, we can obtain the equation that $(x, y)$ satisfies as $x^{2}=(x-1)^{2}+y^{2}$, which simplifies to $y^{2}=2 x-1$. Therefore, the locus of $P$ is a parabola.