Let and be three points on the parabola and let the line segment meet the line through parallel to t

Q: JEE Main 2023 Conic Sections: Let and be three points on the parabola and let the line segment meet the line through parallel to t...

The correct answer is 1. This problem is a classic example of how parametric representation simplifies calculations in coordinate geometry, especially for conic sections like parabolas. The key is to express all points and derived geometric properties in terms of the parameters, which often leads to elegant cancellations. --- **1. Introduction: Parametric Representation of a Parabola** The most efficient way to approach problems involving points on a parabola, particularly when dealing with chords, tangents, and geometr

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Let and be three points on the parabola and let the line segment meet the line through parallel to the -axis at the point . Let and respectively be the feet of the perpendiculars from and on . Then is equal to .

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This problem is a classic example of how parametric representation simplifies calculations in coordinate geometry, especially for conic sections like parabolas. The key is to express all points and derived geometric properties in terms of the parameters, which often leads to elegant cancellations.

1. Introduction: Parametric Representation of a Parabola

The most efficient way to approach problems involving points on a parabola, particularly when dealing with chords, tangents, and geometric relationships, is by using parametric coordinates. This method reduces the number of variables and often reveals underlying symmetries and simplifications.

The given parabola is $y^2 = 6x$ . The standard form of a parabola with its vertex at the origin and axis along the x-axis is $y^2 = 4ax$ . By comparing $y

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