19. Given the quadratic equation $z^{2}-2(4 \operatorname{tg} \theta+3) z$ $+25 \sec ^{2} \theta=0$ with roots corresponding to points $F_{1}, F_{2}$ on the complex plane, then when $\theta$ takes all real values in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, the ordinary equation of the trajectory of the endpoints of the major axis of the ellipse with foci at $F_{1}, F_{2}$ and passing through the origin is $\qquad$ -
19. $\frac{y^{2}}{25}-\frac{(x-3)^{2}}{16}=1$