Question:
<p>If the foci and vertices of an ellipse be (<span class="math-tex">\(\pm\)</span>1, 0) and (<span class="math-tex">\(\pm\)</span>2, 0), then the minor axis of the ellips is:</p>
<p style="display:inline">2</p>
<p style="display:inline"><span class="math-tex">\(2\sqrt{3}\)</span></p>
<p style="display:inline">4</p>
<p style="display:inline"><span class="math-tex">\(2\sqrt{5}\)</span></p>
Step-by-Step Solution
Key Concept: Use the coordinates of the foci (±ae, 0) and vertices (±a, 0) to determine the semi-major axis $a$ and semi-minor axis $b$ via the eccentricity relation.
<p>ae = 1, a = 2, e = <span class="math-tex">\(\frac{1}{2}\)</span><br />
<span class="math-tex">\(\Rightarrow\)</span> b = <span class="math-tex">\(\sqrt{4\left(1-\frac{1}{4}\right)}=\sqrt{3}\)</span><br />
Hence minor axis = <span class="math-tex">\(2\sqrt{3}\)</span></p>
Correct Answer: B