7. Let $a$ be a non-zero real number. In the Cartesian coordinate system $x O y$, the focal distance of the quadratic curve $x^{2}+a y^{2}+a^{2}=0$ is 4, then the value of $a$ is
According to the problem, $a<0, x^{2}+a y^{2}+a^{2}=0 \Rightarrow \frac{y^{2}}{-a}-\frac{x^{2}}{a^{2}}=1 \Rightarrow -a+a^{2}=4$ $\Rightarrow a^{2}-a-4=0 \Rightarrow a=\frac{1-\sqrt{17}}{2}$.