The normal to the curve x² = 4y passing through (1, 2) is:

The normal to the curve x² = 4y passing through (1, 2) is:

• A. x + y = 3
• B. x − y = 1
• C. x + y = 1
• D. x − y = −1

Answer: A) x + y = 3

Explanation: x² = 4y → 2x = 4 dy/dx → dy/dx = x/2. Slope of normal = −2/x. Let point on curve be (x₁, y₁). Normal eq: y − y₁ = (−2/x₁)(x − x₁). It passes through (1, 2). Also y₁ = x₁²/4. Substitute: 2 − x₁²/4 = (−2/x₁)(1 − x₁). Multiply by 4x₁: 8x₁ − x₁³ = −8(1 − x₁) = −8 + 8x₁ → −x₁³ = −8 → x₁³ = 8 → x₁ = 2. Then y₁ = 1. Normal eq through (2, 1) with slope −2/2 = −1: y − 1 = −1(x − 2) → y − 1 = −x + 2 → x + y = 3.