If the line intersects the parabola at the points and , then at the vertex of the parabola, the line

Q: JEE Main 2021 Conic Sections: If the line intersects the parabola at the points and , then at the vertex of the parabola, the line...

The correct answer is A. Here's a detailed and educational solution to the problem, designed to be clear and comprehensive for a JEE aspirant. --- **1. Understanding the Problem and Key Concepts** We are asked to determine the angle subtended by the line segment AB at the vertex of a given parabola. The line segment AB is the chord formed by the intersection of a specific line and the parabola. To solve this problem effectively, we will utilize the following key mathematical concepts: * **Vertex of a Parabola:** The tur

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If the line intersects the parabola at the points and , then at the vertex of the parabola, the line segment AB subtends an angle equal to

Accepted Answer

Here's a detailed and educational solution to the problem, designed to be clear and comprehensive for a JEE aspirant.

1. Understanding the Problem and Key Concepts

We are asked to determine the angle subtended by the line segment AB at the vertex of a given parabola. The line segment AB is the chord formed by the intersection of a specific line and the parabola.

To solve this problem effectively, we will utilize the following key mathematical concepts:

Vertex of a Parabola: The turning point of the parabola. For standard forms like $x^2=4ay$ or $y^2=4ax$ , the vertex is at the origin $(0,0)$ .
Homogenization of a Second-Degree Curve: A powerful technique to find the combined

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