<p>Find the length of the transverse axis of the rectangular hyperbola <i>xy</i> = 18.</p>
Step-by-Step Solution
Key Concept: For a rectangular hyperbola in the form xy = c, the transverse axis length is 2a where a² = 2c.
<p><strong>Step 1:</strong> Compare with the standard form $xy = \frac{a^2}{2}$</p><p><strong>Step 2:</strong> From <i>xy</i> = 18, we get $\frac{a^2}{2} = 18$</p><p><strong>Step 3:</strong> Solve for <i>a</i>: <i>a</i>² = 36, so <i>a</i> = 6</p><p><strong>Step 4:</strong> The length of transverse axis = 2<i>a</i> = 2 × 6 = 12</p>
Correct Answer: 12