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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

Given equation: \(2 x^2+3 x y+y^2=0\) Compare with \(a x^2 + 2h x y + b y^2 = 0\): \(a=2, 2h=3 \Rightarrow h=\frac{3}{2}, b=1\) \(\left|\tan \left(\theta_1-\theta_2\right)\right|=\left|\frac{2\sqrt{h^2-ab}}{a+b}\right|\)…