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AP EAMCET · Maths · Pair of Lines

If the pair of lines \(2 x^2+3 x y+y^2=0\) makes angles \(\theta_1\) and \(\theta_2\) with the positive direction of the X-axis, then \(\left|\tan \left(\theta_1-\theta_2\right)\right|=\)

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

Answer & Solution

Correct Answer

(B) \(\frac{1}{3}\)

Step-by-step Solution

Detailed explanation

\( a=2, h=\frac{3}{2}, b=1 \) \( \left|\tan \left(\theta_1-\theta_2\right)\right| = \left|\frac{2\sqrt{h^2-ab}}{a+b}\right| \) \( = \left|\frac{2\sqrt{(\frac{3}{2})^2-(2)(1)}}{2+1}\right| \) \( = \left|\frac{2\sqrt{\frac{9}{4}-2}}{3}\right| \)…