Question:
<p>The equation of the ellipse whose vertices are (<span class="math-tex">\(\pm\)</span>5, 0) and foci are (<span class="math-tex">\(\pm\)</span>4, 0) is</p>
<p style="display:inline">3x<sup>2</sup> + 4y<sup>2</sup> = 192</p>
<p style="display:inline">25x<sup>2</sup> + 9y<sup>2</sup> = 225</p>
<p style="display:inline">4x<sup>2</sup> + 3y<sup>2</sup> = 192</p>
<p style="display:inline">9x<sup>2</sup> + 25y<sup>2</sup> = 225</p>
Step-by-Step Solution
Key Concept: Identify the semi-major axis $a$ and focal distance $c$ from the given coordinates and use the relation $b^2 = a^2 - c^2$ to find the semi-minor axis for the standard equation.
<p>9x<sup>2</sup> + 25y<sup>2</sup> = 225</p>
Correct Answer: D