Let the tangent and normal at the point on the ellipse meet the -axis at the points and respectively

Q: JEE Main 2023 Conic Sections: Let the tangent and normal at the point on the ellipse meet the -axis at the points and respectively...

The correct answer is A. This problem is a comprehensive test of concepts involving ellipses, tangents, normals, circles, and poles/polars. We will systematically break down the problem into several parts to ensure clarity and accuracy. **1. Finding the Equation of the Tangent to the Ellipse and its y-intercept A** * **Key Concept:** The equation of the tangent to the ellipse at a point is given by the formula , which is . This formula is a fundamental result

Question

Let the tangent and normal at the point on the ellipse meet the -axis at the points and respectively. Let the circle be drawn taking as a diameter and the line intersect at the points and . If the tangents at the points and on the circle intersect at the point , then is equal to :

Accepted Answer

This problem is a comprehensive test of concepts involving ellipses, tangents, normals, circles, and poles/polars. We will systematically break down the problem into several parts to ensure clarity and accuracy.

1. Finding the Equation of the Tangent to the Ellipse and its y-intercept A

Key Concept: The equation of the tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ at a point $(x_1, y_1)$ is given by the formula $T=0$ , which is $\frac{x x_1}{a^2} + \frac{y y_1}{b^2} = 1$ . This formula is a fundamental result

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61

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60

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