Question:
<p>If the line y - <span class="math-tex">\(\sqrt 3\)</span>x + 3 = 0 cut the parabola y<sup>2</sup> = x + 2 at A and B, then the value of PA <span class="math-tex">\(\cdot\)</span> PB is: [where P = (<span class="math-tex">\(\sqrt 3\)</span>, 0)].</p>
<p style="display:inline"><span class="math-tex">\(\frac{4(2 \ + \ \sqrt{3})}{\sqrt 3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{4(2 \ - \ \sqrt{3})}{\sqrt 3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{4(2 \ + \ \sqrt{3})}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{4(2 \ - \ \sqrt{3})}{3}\)</span></p>
Step-by-Step Solution
Key Concept: Use the parametric form of the line equation passing through point P to transform the intersection problem into a quadratic equation in distance r.
<p><span class="math-tex">$\frac{4(2 \ + \ \sqrt{3})}{3}$</span></p>
Correct Answer: C