7. Let the line $l$ passing through the fixed point $M(a, 0)$ intersect the parabola $y^{2}=4 x$ at points $P, Q$. If $\frac{1}{|P M|^{2}}+\frac{1}{|Q M|^{2}}$ is a constant, then the value of $a$ is $\qquad$ .
Answer 2.
Solution Let the parametric equation of the line $l$ be $\left\{\begin{array}{l}x=a+t \cos \alpha \\ y=t \sin \alpha\end{array}\right.$ (where $t$ is the parameter, $\alpha$ is the angle of inclination and $\left.\alpha \in(0, \pi)\right)$, substituting into the parabola equation yields:
$$
t^{2} \sin ^{2} \alpha-4 t \cos \alpha-4 a=0
$$

Let the two roots of this equation be $t_{1}, t_{2}$, then
$$
t_{1}+t_{2}=\frac{4 \cos \alpha}{\sin ^{2} \alpha}, \quad t_{1} \cdot t_{2}=\frac{4 a}{\sin ^{2} \alpha}
$$

Then
$$
\frac{1}{|P M|^{2}}+\frac{1}{|P Q|^{2}}=\frac{1}{t_{1}^{2}}+\frac{1}{t_{2}^{2}}=\frac{t_{1}^{2}+t_{2}^{2}}{\left(t_{1} t_{2}\right)^{2}}=\frac{\left(t_{1}+t_{2}\right)^{2}-2 t_{1} t_{2}}{\left(t_{1} t_{2}\right)^{2}}=\frac{\frac{16 \cos ^{2} \alpha}{\sin ^{4} \alpha}+\frac{8 a}{\sin ^{2} \alpha}}{\frac{16 a^{2}}{\sin ^{4} \alpha}}=\frac{2 \cos ^{2} \alpha+a \sin ^{2} \alpha}{2 a^{2}} \text { is a constant }
$$

Therefore, $a=2$.