Mathematics

The key is to convert each conic to standard form and extract its eccentricity using the relationship between $a$, $b$, and $c$. For an ellipse, $c^2 = a^2 - b^2$; for a hyperbola, $c^2 = a^2 + b^2$. Once you identify which axis is major (or transverse) for each curve, you can find $e = c/a$ and multiply them together.

The key is to convert each conic to standard form and extract its eccentricity using the relationship between $a$, $b$, and $c$. For an ellipse, $c^2 = a^2 - b^2$; for a hyperbola, $c^2 = a^2 + b^2$. Once you identify which axis is major (or transverse) for each curve, you can find $e = c/a$ and multiply them together.