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Coordinate Geometry
Parabola, Tangents
jee_main_2026_april_5_shift_1
Grade 12

Question:

The tangent to the parabola y² = 4x at the point (1, 2) meets the x-axis at P. Find the distance from P to the vertex of the parabola.
A. 1
B. 2
C. 3
D. 4

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. Step 3: x-intercept: y = 0 => x = -1, so P = (-1, 0). Step 4: Vertex of parabola = (0, 0). Distance = 1.
Correct Answer: A
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