Let P be a point on the parabola, y 2 = 12x and N be the foot of the perpendicular drawn from P on t

Q: JEE Main 2020 Conic Sections: Let P be a point on the parabola, y 2 = 12x and N be the foot of the perpendicular drawn from P on t...

The correct answer is A. This problem requires a deep understanding of the coordinate geometry of parabolas, including parametric representation, properties of the axis, midpoint formula, and linear equations. We will systematically break down the problem into smaller, manageable steps. **1. Understanding the Parabola and Parametric Representation** The given parabola is . **Key Concept:** The standard form of a parabola with its vertex at the origin and opening to the right is . Comparing with , we find , which implies

Question

Let P be a point on the parabola, y 2 = 12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is , then :

Accepted Answer

This problem requires a deep understanding of the coordinate geometry of parabolas, including parametric representation, properties of the axis, midpoint formula, and linear equations. We will systematically break down the problem into smaller, manageable steps.

1. Understanding the Parabola and Parametric Representation

The given parabola is $y^2 = 12x$ . Key Concept: The standard form of a parabola with its vertex at the origin and opening to the right is $y^2 = 4ax$ . Comparing $y^2 = 12x$ with $y^2 = 4ax$ , we find $4a = 12$ , which implies $a=3$ .

Key Concept: The axis of the parabola $y^2 = 4ax$ is

Answer

MQ =

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PN = 4

Answer

PN = 3

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MQ =

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Solution

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