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Question #40827

Difficulty: 8/10 | 🟢 Free

The Question

A closed curve $C$ is defined by the equation $y^2 + 4|x| = 20$ . A light ray originates from the point $M(0, 2)$ and travels parallel to the negative x-axis. It strikes the inner surface of $C$ at point $A$ and undergoes continuous reflections. Let $P$ be the polygon formed by the sequence of all distinct points of incidence on $C$ . Find the area of $P$ .

Options

A.
16
B.
24
C.
32
D.
40

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Reflective Property|Latus Rectum Geometry|The Modulus Trap

Why This Question Is Tricky

Common Mistakes

This question tests the reflective property of parabolas combined with a 'Modulus Trap'.

Students often struggle with absolute value loci, attempting to treat $y^2 + 4|x| = 20$ as a single non-standard curve and applying brute-force calculus to find normals.

The trap forces them to decompose the locus into two distinct parabolas facing each other.

By tracing the ray, students must apply the reflective property sequentially: rays parallel to the axis reflect through the focus, and rays passing through the focus reflect parallel to the axis.

Beautifully, the points of incidence perfectly map to the endpoints of the latus recta of both parabolas, rewarding students who recognize the geometric significance of the coordinates.

Quick Facts About This Question

Question Information

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