Multiple choice

The angle between the lines represented by the equation (x^2 + 2xy \cot\theta - y^2 = 0) is:

  1. 30o

  2. 45o

  3. 60o

  4. 90o
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D Correct answer
Explanation

The equation x² + 2xy cotθ - y² = 0 represents two lines through origin. For homogeneous equation Ax² + 2Hxy + By² = 0, the angle φ between lines satisfies tanφ = 2√(H² - AB)/|A+B|. Here A=1, H=cotθ, B=-1. tanφ = 2√(cot²θ + 1)/|1-1| = 2√(cosec²θ)/0 = 2cosecθ/0 → ∞, so φ = 90°. The lines are perpendicular.

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