<p>A point of the curve <span class="math-tex">\(\frac{x^{2}}{A^{2}}-\frac{y^{2}}{B^{2}}=1\)</span> is</p>
<p style="display:inline">(A sec <span class="math-tex">\(\theta\)</span>, B tan <span class="math-tex">\(\theta\)</span>)</p>
<p style="display:inline">(A sec<sup>2</sup> <span class="math-tex">\(\theta\)</span>, B tan<sup>2</sup> <span class="math-tex">\(\theta\)</span>)</p>
<p style="display:inline">(A cos<sup>2</sup> <span class="math-tex">\(\theta\)</span>, B sin<sup>2</sup> <span class="math-tex">\(\theta\)</span>)</p>
<p style="display:inline">(A cos <span class="math-tex">\(\theta\)</span>, B sin <span class="math-tex">\(\theta\)</span>)</p>
Step-by-Step Solution
Key Concept: The parametric form of a hyperbola $\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1$ is $(A\sec\theta, B\tan\theta)$, derived from the identity $\sec^2\theta - \tan^2\theta = 1$ which matches the hyperbola equation structure when substituted.
<p>(A sec <span class="math-tex">$\theta$</span>, B tan <span class="math-tex">$\theta$</span>)</p>
Correct Answer: A