Points $F$, $G$, and $H$ are collinear with $G$ between $F$ and $H$. The ellipse with foci at $G$ and $H$ is internally tangent to the ellipse with foci at $F$ and $G$, as shown below. The two ellipses have the same eccentricity $e$, and the ratio of their areas is $2025$. (Recall that the eccentricity of an ellipse is $e = \tfrac{c}{a}$, where $c$ is the distance from the center to a focus, and $2a$ is the length of the major axis.) What is $e$? $\textbf{(A)}~\frac35\qquad$ $\textbf{(B)}~\frac{16}{25}\qquad$ $\textbf{(C)}~\frac45\qquad$ $\textbf{(D)}~\frac{22}{23}\qquad$ $\textbf{(E)}~\frac{44}{45}$