3. Let the circular cone $S O$ be an equilateral cone, $S A B$ be the axial section, and $S A=2$. If point $M$ is the midpoint of $S O$, and the moving point $P$ is on the plane of the base of the cone, such that $M P$ makes a $60^{\circ}$ angle with $S A$, in the plane of the base of the cone, if the $x$-axis is established with $A B$ and $O$ as the origin, then the trajectory of point $P$ is
3. $y^{2}=-3 x+\frac{3}{2}$

Let $P(x, y)$. Since the midpoint of $O A$ is $C$
$$
\begin{array}{l}
\left(-\frac{1}{2}, 0\right),|M C|=1 \text { and }|P C|= \\
\sqrt{\left(x+\frac{1}{2}\right)^{2}+y^{2}},|M P|=\sqrt{x^{2}+y^{2}+\frac{3}{4}}
\end{array}
$$

From $\angle P M C=60^{\circ}$ and the cosine rule, we can get.