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AP EAMCET · Maths · Pair of Lines

If the slope of one of the lines represented by \(2 x^2+3 x y+k y^2=0\) is 2, then the angle between the pair of lines is

  1. A \(\frac{\pi}{2}\)
  2. B \(\frac{\pi}{3}\)
  3. C \(\frac{\pi}{6}\)
  4. D \(\frac{\pi}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

The slopes \(m\) of the lines are given by \(k m^2 + 3 m + 2 = 0\). Substitute \(m = 2\): \(k(2)^2 + 3(2) + 2 = 0\). \(4k + 6 + 2 = 0 \Rightarrow 4k = -8 \Rightarrow k = -2\). The product of the slopes \(m_1 m_2 = \frac{a}{b} = \frac{2}{k} = \frac{2}{-2} = -1\). Since…