Question:
<p>The equations of the directrices of the ellipse 16x<sup>2</sup> + 25y<sup>2</sup> = 400 are:</p>
<p style="display:inline">5x = <span class="math-tex">\(\pm\)</span>9</p>
<p style="display:inline">3x = <span class="math-tex">\(\pm\)</span>10</p>
<p style="display:inline">2x = <span class="math-tex">\(\pm\)</span>25</p>
<p style="display:inline">None of these</p>
Step-by-Step Solution
Key Concept: Transform the ellipse equation to standard form to identify the major axis and eccentricity, then apply the directrix formula $x = \pm a/e$.
<p><span class="math-tex">$\frac{x^{2}}{25}+\frac{y^{2}}{16}$</span> = 1<br />
<span class="math-tex">$\Rightarrow$</span> e = <span class="math-tex">$\sqrt{1-\frac{16}{25}}=\frac{3}{5}$</span><br />
Therefore, directrices are x <span class="math-tex">$\pm \frac{5}{\frac 3 5}$</span> = 0 or 3x <span class="math-tex">$\pm$</span> 25 = 0</p>
Correct Answer: D