Question:
<p>A hyperbola passes through the points (3, 2) and (-17, 12) and has its centre at origin and transverse axis is along x-axis. The length of its transverse axis is</p>
<p style="display:inline">4</p>
<p style="display:inline">2</p>
<p style="display:inline">8</p>
<p style="display:inline">6</p>
Step-by-Step Solution
Key Concept: Substitute the given points into the standard hyperbola equation to solve for the semi-axis parameters using a system of linear equations.
<p>Let the equation of hyperbola be <span class="math-tex">$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$</span><br />
This hyperbola passes through (3, 2).<br />
<span class="math-tex">$\Rightarrow \frac{9}{a^{2}}-\frac{4}{b^{2}}=1$</span> ...(i)<br />
Also, it passes through (-17, 12).<br />
<span class="math-tex">$\Rightarrow \frac{(-17)^{2}}{a^{2}}-\frac{(12)^{2}}{b^{2}}=1$</span> ...(ii)<br />
Solving (i) and (ii), we get a = 1 and <span class="math-tex">$b=\frac{1}{\sqrt{2}}$</span><br />
Hence, length of transverse axis = 2a = 2</p>
Correct Answer: B