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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 lines represented by \(2 x^2+3 x y+k y^2=0\) satisfy \(k m^2 + 3m + 2 = 0\). Given \(m=2\): \(k(2)^2 + 3(2) + 2 = 0 \Rightarrow 4k + 8 = 0 \Rightarrow k = -2\). The equation becomes \(2 x^2+3 x y-2 y^2=0\). Comparing with \(a x^2 + 2h x y + b y^2 = 0\), we…