Question 14
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 $e = \dfrac{c}{a},$ where $c$ is the distance from the center to a focus, and $2a$ is the length of the major axis.) What is $e?$
The two ellipses have the same eccentricity $e,$ and the ratio of their areas is $2025.$ (Recall that the eccentricity of an ellipse is $e = \dfrac{c}{a},$ where $c$ is the distance from the center to a focus, and $2a$ is the length of the major axis.) What is $e?$