Question:
<p>If (0, <span class="math-tex">\(\pm\)</span>4) and (0, <span class="math-tex">\(\pm\)</span>2) be the foci and vertices of a hyperbola, then its equation is</p>
<p style="display:inline"><span class="math-tex">\(\frac{x^{2}}{4}-\frac{y^{2}}{12}=1\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{x^{2}}{12}-\frac{y^{2}}{4}=1\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{y^{2}}{12}-\frac{x^{2}}{4}=1\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{y^{2}}{4}-\frac{x^{2}}{12}=1\)</span></p>
Step-by-Step Solution
Key Concept: Identify the hyperbola as vertical since the foci and vertices lie on the y-axis and use the relation $c^2 = a^2 + b^2$ to determine the equation parameters.
<p><span class="math-tex">$\frac{y^{2}}{4}-\frac{x^{2}}{12}=1$</span></p>
Correct Answer: D