GATE AG 2012 • Q2 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

The line y = x - 1 can be expressed in polar coordinates (r, θ) as:

Options:

  • (A) r = cos θ
  • (B) r = sin θ
  • (C) r(cos θ + sin θ) = 1
  • (D) r(cos θ - sin θ) = 1

Official Answer Key:

D

Step-by-Step Solution & Explanation

Substitute x = r cos θ, y = r sin θ into y = x - 1: r sin θ = r cos θ - 1, i.e. r cos θ - r sin θ = 1, so r(cos θ - sin θ) = 1. Answer: D.

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