Let the tangent to the parabola at the point be perpendicular to the line . Then the square of dista

Q: JEE Main 2023 Conic Sections: Let the tangent to the parabola at the point be perpendicular to the line . Then the square of dista...

The correct answer is 3. This problem is a comprehensive test of your understanding of conic sections, specifically parabolas and hyperbolas, along with fundamental concepts of coordinate geometry like tangents, normals, perpendicular lines, and distance formulas. We will break down the problem into logical steps, applying relevant formulas and concepts at each stage to determine the square of the required distance. --- ### **Problem Overview** Our goal is to find the square of the distance of a given point from a speci

Question

Let the tangent to the parabola at the point be perpendicular to the line . Then the square of distance of the point from the normal to the hyperbola at its point is equal to .

Accepted Answer

This problem is a comprehensive test of your understanding of conic sections, specifically parabolas and hyperbolas, along with fundamental concepts of coordinate geometry like tangents, normals, perpendicular lines, and distance formulas. We will break down the problem into logical steps, applying relevant formulas and concepts at each stage to determine the square of the required distance.

Problem Overview

Our goal is to find the square of the distance of a given point $(6,-4)$ from a specific normal to a hyperbola. To achieve this, we must first:

Determine the value of $\alpha$ : This involves using the properties of the parabola $y^2=12x$ and its tangent at $(3, \alpha)$ , along with the condition that this tangent is perpendicular to the line

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Solution

Problem Overview

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