Let P be a variable point on the parabola . Then, the locus of the mid-point of the point P and the

Q: JEE Main 2024 Conic Sections: Let P be a variable point on the parabola . Then, the locus of the mid-point of the point P and the ...

The correct answer is A. This problem requires us to find the locus of a midpoint, which involves a systematic application of coordinate geometry concepts: parameterization of points, finding the foot of a perpendicular, using the midpoint formula, and finally eliminating the parameter. **1. Key Concepts and Formulas** * **Parametric Representation:** A point on a curve can often be represented using a single parameter (e.g., ). For a parabola , a point P can be . * **Foot of the Perpendicular:** The foot of the perpend

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Let P be a variable point on the parabola . Then, the locus of the mid-point of the point P and the foot of the perpendicular drawn from the point P to the line y = x is :

Accepted Answer

This problem requires us to find the locus of a midpoint, which involves a systematic application of coordinate geometry concepts: parameterization of points, finding the foot of a perpendicular, using the midpoint formula, and finally eliminating the parameter.

1. Key Concepts and Formulas

Parametric Representation: A point on a curve can often be represented using a single parameter (e.g., $t$ ). For a parabola $y = ax^2 + c$ , a point P can be $(t, at^2+c)$ .
Foot of the Perpendicular: The foot of the perpendicular from a point $P(x_1, y_1)$ to a line $ax + by + c = 0$ is a point $Q(x_2, y_

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