11. Let $P$ be a moving point on the parabola $y=x^{2}$, and the symmetric point of a fixed point $A(a, 0)$ about point $P$ is $Q(a \neq 0)$. Then the equation of the trajectory of point $Q$ is $\qquad$.
11. $y=\frac{1}{2}(x+a)^{2}$. Hint: Let $Q(x, y)$, then $P\left(\frac{x+a}{2}, \frac{y}{2}\right)$. Since $P$ is on the parabola $y=x^{2}$, the equation of the locus of point $Q$ is $y=\frac{1}{2}(x+a)^{2}$.