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Coordinate Geometry

Parabola, Tangents

jee_main_2026_jan_22_shift_1

Grade None

Question:

The equation of the tangent to the parabola y² = 4x at the point (1, 2) is:

A. y = x + 1

B. y = 2x

C. y = x + 2

D. y = 2x + 1

Step-by-Step Solution

Key Concept: Tangent to y² = 4ax at (x₁, y₁) is yy₁ = 2a(x + x₁).

Step 1: y² = 4x => a = 1. Step 2: Tangent at (1, 2): 2y = 2(x + 1) => y = x + 1.

Correct Answer: A

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