Question:
<p>The straight lines y = <span class="math-tex">\(\pm\)</span>x intersect the parabola y<sup>2</sup> = 8x at points P and Q, then length of PQ is</p>
<p style="display:inline">8</p>
<p style="display:inline">4</p>
<p style="display:inline">16</p>
<p style="display:inline"><span class="math-tex">\(4 \sqrt{2}\)</span></p>
Step-by-Step Solution
Key Concept: Find the intersection points by solving the equations of the lines and the parabola simultaneously, then calculate the distance between these points using the distance formula.
<p>Given, y = <span class="math-tex">$\pm$</span>x ...(i)<br />
and y<sup>2</sup> = 8x ...(ii)<br />
Solving (i) and (ii),<br />
the point of intersection are P(8, 8) and Q(8, -8)<br />
<img alt="" height="114" src="https://i.imgur.com/71bFGIj.png" width="131" /><br />
<span class="math-tex">$\therefore$</span> Length of PQ <span class="math-tex">$=\sqrt{(8-8)^{2}+(8+8)^{2}}$</span><br />
= 16</p>
Correct Answer: C