Let and be the two points of intersection of the line and the mirror image of the parabola with resp

Q: JEE Main 2023 Conic Sections: Let and be the two points of intersection of the line and the mirror image of the parabola with resp...

The correct answer is 1. This solution will guide you through finding the distance between intersection points and the area of a triangle involving a reflected parabola, focusing on clarity and detailed explanations for each step. --- **Key Concept: Reflection of a Parabola** When a parabola is reflected across a line, its geometric properties are preserved. The reflected curve is still a parabola. Its focus will be the reflection of the original focus, and its directrix will be the reflection of the original directrix.

Question

Let and be the two points of intersection of the line and the mirror image of the parabola with respect to the line . If denotes the distance between and , and a denotes the area of , where is the focus of the parabola , then the value of is .

Accepted Answer

This solution will guide you through finding the distance between intersection points and the area of a triangle involving a reflected parabola, focusing on clarity and detailed explanations for each step.

Key Concept: Reflection of a Parabola

When a parabola is reflected across a line, its geometric properties are preserved. The reflected curve is still a parabola. Its focus will be the reflection of the original focus, and its directrix will be the reflection of the original directrix. This approach simplifies finding the equation of the reflected parabola significantly, as it avoids complex coordinate transformations.

1. Analyze the Original Parabola $y^2 = 4x$

The given parabola is in the standard form $y^2 = 4ax$ . Comparing $y^2 =

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