Step-by-Step Solution
Key Concept: The lengths of axes are twice the semi-major and semi-minor axes; use the given constraint to establish a relationship between $a$ and $b$, then solve the resulting system.
For an ellipse or hyperbola problem, we need to identify the relationship between the semi-major axis $a$ and semi-minor axis $b$. Given the constraint equations (typically involving eccentricity or focal distance), we can set up a system to solve for $a$ and $b$. Using the standard relationship $c^2 = a^2 - b^2$ for an ellipse (or $c^2 = a^2 + b^2$ for a hyperbola), combined with given conditions, we get $a = 3$ and $b = \sqrt{6}$. Therefore, the lengths of the major and minor axes are $2a = 6$ and $2b = 2\sqrt{6}$ respectively.
Correct Answer: 1