Conic Sections
Conic Section
star_batch_jee_advanced_2025
Grade 11
Question:
The area of region of the point $P$ is:
$\sqrt{2}\left(\frac{\pi}{3} - \frac{\sqrt{3}}{4}\right)$
$\sqrt{3}\left(\frac{\pi}{3} - \frac{\sqrt{3}}{4}\right)$
$2\left(\frac{\pi}{3} - \frac{\sqrt{3}}{4}\right)$
$3\left(\frac{\pi}{3} - \frac{\sqrt{3}}{4}\right)$
Step-by-Step Solution
Key Concept: The area equals the difference between a circular sector of angle $60°$ and a triangle, multiplied by a factor of $\sqrt{3}$ that arises from the geometric configuration of the constraint curves.
This problem involves finding the area of a region defined by constraints on point $P$ (typically involving distances or angles from fixed points). The region is bounded by circular arcs and/or lines, creating a lens-shaped or sector-like area. The expression $\frac{\pi}{3} - \frac{\sqrt{3}}{4}$ represents the area of a circular segment (sector minus triangle), where $\frac{\pi}{3}$ is a $60°$ sector and $\frac{\sqrt{3}}{4}$ is the area of an equilateral triangle with appropriate dimensions. The coefficient $\sqrt{3}$ appears from geometric calculations involving the radii and angles of the constraining circles or from the scaling factor of the region.
Correct Answer: 2