Question:
<p>The latus rectum of a parabola whose focal chord PSQ is such that SP = 3 and SQ = 2 is given by:</p>
<p style="display:inline"><span class="math-tex">\(\frac65\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac85\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{12}5\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{24}5\)</span></p>
Step-by-Step Solution
Key Concept: The semi-latus rectum of a parabola is the harmonic mean of the lengths of the segments of any focal chord.
<p>We know that, a, <span class="math-tex">$\frac c2$</span>, b are in GP that means,<br />
<span class="math-tex">$\frac{1}{a}+\frac{1}{b}=\frac{4}{c}$</span><br />
<span class="math-tex">$\frac{1}{3}+\frac{1}{2}=\frac{4}{c}$</span><br />
c = <span class="math-tex">$\frac{24}5$</span></p>
Correct Answer: D