Let be the acute angle between the tangents to the ellipse and the circle at their point of intersec

Q: JEE Main 2021 Conic Sections: Let be the acute angle between the tangents to the ellipse and the circle at their point of intersec...

The correct answer is A. This solution aims to provide a comprehensive, step-by-step guide to solving the problem of finding the angle between tangents to an ellipse and a circle. We will break down the problem into manageable parts, explaining the rationale behind each step and using clear mathematical notation. **1. Understanding the Goal and the Master Formula** The problem asks us to determine the tangent of the acute angle, denoted by , between two lines: the tangent to the given ellipse and the tangent to the give

Question

Let be the acute angle between the tangents to the ellipse and the circle at their point of intersection in the first quadrant. Then tan is equal to :

Accepted Answer

This solution aims to provide a comprehensive, step-by-step guide to solving the problem of finding the angle between tangents to an ellipse and a circle. We will break down the problem into manageable parts, explaining the rationale behind each step and using clear mathematical notation.

1. Understanding the Goal and the Master Formula

The problem asks us to determine the tangent of the acute angle, denoted by $\theta$ , between two lines: the tangent to the given ellipse and the tangent to the given circle. Both tangents are drawn at their common point of intersection located in the first quadrant.

The fundamental formula for finding the acute angle $\theta$ between two lines with slopes $m_1$ and $m_2$ is:

Answer

Answer

Answer

Answer

2

Question

Options

Solution

Practice More Conic Sections Questions