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AP EAMCET · Maths · Pair of Lines

The angle between the straight lines represented by \(\left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2\) is

  1. A \(\frac{\alpha}{2}\)
  2. B \(\alpha\)
  3. C \(2\alpha\)
  4. D \(\frac{\pi}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2\alpha\)

Step-by-step Solution

Detailed explanation

\(\left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2\) \(x^2 \sin^2 \alpha + y^2 \sin^2 \alpha = x^2 \cos^2 \alpha - 2xy \sin \alpha \cos \alpha + y^2 \sin^2 \alpha\) \(x^2 (\sin^2 \alpha - \cos^2 \alpha) + 2xy \sin \alpha \cos \alpha = 0\)…