1. Given $F_{1} 、 F_{2}$ are the left and right foci of the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$, and $A$ is a moving point on the ellipse. Circle $C$ is tangent to the extension of $F_{1} A$, the extension of $F_{1} F_{2}$, and the line segment $A F_{2}$. If $M(t, 0)$ is a point of tangency, then $t=$ $\qquad$ .
1.2.

Analysis: Circle $C$ is the excircle of $\triangle A F_{1} F_{2}$ corresponding to side $A F_{2}$. Let circle $C$ touch $F_{1} A$ at $M_{1}$, then $F_{1} M_{1}=F_{1} M$ and $F_{1} M+F_{1} M_{1}=F_{1} F_{2}+A F_{2}+A F_{1}=6$, which gives $F_{1} M=3$, thus $M(2,0)$, i.e., $t=2$.