Let be the lines passing through the point and touching the parabola . Let and be the points on the

Q: JEE Main 2024 Conic Sections: Let be the lines passing through the point and touching the parabola . Let and be the points on the ...

The correct answer is 9. This problem elegantly combines concepts of parabolas, tangents, and properties of isosceles triangles. We'll start by standardizing the parabola's equation, then find the equations of the tangent lines from the given point, and finally use the geometric properties of the isosceles triangle to determine the slopes of the base. --- **1. Standardizing the Parabola Equation** **Concept:** To work effectively with a parabola, we often transform its general equation into a standard form, typically or

Question

Let be the lines passing through the point and touching the parabola . Let and be the points on the lines and such that the is an isosceles triangle with base . If the slopes of the lines are and , then is equal to .

Accepted Answer

This problem elegantly combines concepts of parabolas, tangents, and properties of isosceles triangles. We'll start by standardizing the parabola's equation, then find the equations of the tangent lines from the given point, and finally use the geometric properties of the isosceles triangle to determine the slopes of the base.

1. Standardizing the Parabola Equation

Concept: To work effectively with a parabola, we often transform its general equation into a standard form, typically $(x-h)^2 = 4a(y-k)$ or $(y-k)^2 = 4a(x-h)$ . This helps identify the vertex, axis, and focal length, which are crucial for subsequent calculations.

Step-by-step working: The given equation of the

Question

Solution

Practice More Conic Sections Questions