3. The moving line $l$ intersects the $y$-axis at $A$, and the $x$-axis at $B$. Let the area of $\triangle A O B$ be a constant $S$. A perpendicular is drawn from the origin $O$ to $l$, with the foot of the perpendicular being $P(x, y)$. Then the equation of the locus of point $P$ is $\qquad$
3. $\left(x^{2}+y^{2}\right)^{2}=2 S|x y|$.

Let the equation of $l$ be $y=k x+b$. Then $A(0, b), B\left(-\frac{b}{k}, 0\right)$.
From $\frac{1}{2}\left|b \cdot\left(-\frac{b}{k}\right)\right|=S, b^{2}=2|k| S$, we know that the equation of $O P$ is $y=-\frac{1}{k} x$.
By multiplying the equations of $l$ and $O P$, we get $y(y-b)=-x^{2}$, i.e., $x^{2}+y^{2}=b y$, so $\left(x^{2}+y^{2}\right)^{2}=b^{2} y^{2}=2|k| S y^{2}$.
Substituting $k=-\frac{x}{v}$, we get $\left(x^{2}+y^{2}\right)^{2}=2 S|x y|$.