Question:
<p>The eccentricity of a hyperbola passing through the points (3, 0), (3<span class="math-tex">\(\sqrt 2\)</span>, 2) will be:</p>
<p style="display:inline"><span class="math-tex">\(\sqrt {13}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac {\sqrt {13}}3\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac {\sqrt {13}}2\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac {\sqrt {13}}4\)</span></p>
Step-by-Step Solution
Key Concept: Use the standard form of hyperbola x²/a² - y²/b² = 1 and substitute the two given points to find a and b. Then apply the eccentricity formula e = √(1 + b²/a²) for a hyperbola with horizontal transverse axis.
<p><span class="math-tex">$\frac{9}{a^{2}}$</span> = 1<br />
a = 3 and <span class="math-tex">$\frac{18}{a^{2}}-\frac{4}{b^{2}}$</span> = 1<br />
b<sup>2</sup> = 4<br />
Therefore, e = <span class="math-tex">$\sqrt{1+\frac{4}{9}}=\frac{\sqrt{13}}{3}$</span></p>
Correct Answer: B