P and Q are two distinct points on the parabola, y 2 = 4x, with parameters t and t 1 respectively. I

Q: JEE Main 2020 Conic Sections: P and Q are two distinct points on the parabola, y 2 = 4x, with parameters t and t 1 respectively. I...

The correct answer is A. Here's a detailed, step-by-step solution designed to be clear, elaborate, and educational, addressing the problem and the discrepancy in the provided answer. --- **1. Understanding the Parabola and Parametric Form** The given equation of the parabola is . This is a standard form parabola , where we can identify . For a parabola , the parametric coordinates of any point on it are given by . Since for our parabola, the parametric coordinates of a point are . **Why use parametric form?** Parametric

Question

P and Q are two distinct points on the parabola, y 2 = 4x, with parameters t and t 1 respectively. If the normal at P passes through Q, then the minimum value of is :

Accepted Answer

Here's a detailed, step-by-step solution designed to be clear, elaborate, and educational, addressing the problem and the discrepancy in the provided answer.

1. Understanding the Parabola and Parametric Form

The given equation of the parabola is $y^2 = 4x$ . This is a standard form parabola $y^2 = 4ax$ , where we can identify $a=1$ .

For a parabola $y^2 = 4ax$ , the parametric coordinates of any point on it are given by $(at^2, 2at)$ . Since $a=1$ for our parabola, the parametric coordinates of a point are $(t^2, 2t)$ .

Why use parametric form? Parametric representation is incredibly

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