Question:
<p>The length of the latus rectum of the ellipse 5x<sup>2</sup> + 9y<sup>2</sup> = 45 is</p>
<p style="display:inline"><span class="math-tex">\(\frac{\sqrt{5}}{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{{10}}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{\sqrt{5}}{4}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{{5}}{3}\)</span></p>
Step-by-Step Solution
Key Concept: Transform the ellipse equation into the standard form $ rac{x^2}{a^2} + rac{y^2}{b^2} = 1$ to identify the semi-major axis $a$ and semi-minor axis $b$ for the latus rectum formula $ rac{2b^2}{a}$.
<p><span class="math-tex">$\frac{{10}}{3}$</span></p>
Correct Answer: B