<p>The extremities of the latus rectum of parabola P are:</p>
<p>(a) \(\left(\frac{a}{2}, \frac{(\sqrt{3} + 2\sqrt{3})a}{2}\right), \left(\frac{(\sqrt{3} + 2\sqrt{3})a}{2}, \frac{a}{2}\right)\)</p>
<p>(b) \(\left(-\frac{a}{2}, \frac{(\sqrt{3} - \sqrt{3})a}{2}\right), \left(\frac{(\sqrt{3} - \sqrt{3})a}{2}, -\frac{a}{2}\right)\)</p>
<p>(c) \(\left(\frac{a}{2}, \frac{(\sqrt{3} - \sqrt{3})a}{2}\right), \left(\frac{(\sqrt{3} - \sqrt{3})a}{2}, \frac{a}{2}\right)\)</p>
<p>(d) \(\left(-\frac{a}{2}, \frac{(\sqrt{3} + 2\sqrt{3})a}{2}\right), \left(\frac{(\sqrt{3} + 2\sqrt{3})a}{2}, -\frac{a}{2}\right)\)</p>
Step-by-Step Solution
Key Concept: The latus rectum passes through the focus perpendicular to the axis of symmetry and has length \(4a\) for a parabola.
<p>The latus rectum of a parabola is perpendicular to its axis and passes through the focus. Using the focus and the axis of parabola P, the endpoints of the latus rectum are calculated.</p>
Correct Answer: c