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Question #40821

Difficulty: 8/10 | 🟢 Free

The Question

Let $A$ be the area of the region in the first quadrant bounded by the ellipse $5x^2 - 6xy + 5y^2 = 8$ and the lines $y = 3x$ and $y = (7+4\sqrt{3})x$ . The value of $\frac{36A}{\pi}$ is:

Options

A.
2
B.
3
C.
4
D.
6

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Bridge

Practice problems that bridge the gap between foundational theory and advanced practical application.

Concepts Behind This Question

Diameter of Conics|Axis of Integration Selection|Standard Ellipse/Circle Area

Why This Question Is Tricky

Common Mistakes

This problem tests the 'Axis of Integration Selection' heuristic combined with the properties of rotated conics.

Students who attempt to integrate directly in the Cartesian $(x,y)$ plane will face a non-elementary integral involving the roots of a general quadratic, leading to a massive algebraic bottleneck.

The trap penalizes brute-force integration.

The optimal path requires geometric foresight: recognizing the symmetry of the conic, applying an orthogonal transformation (rotation) to align the axes, and using the eccentric angle parameterization to compute the sector area trivially.

This evaluates the student's ability to choose the correct coordinate system, a hallmark of JEE Advanced.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Conic Sections - Class 11
Concept	Diameter of Conics
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free