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AP EAMCET · Maths · Pair of Lines

If the angle between the pair of lines \(2 x^2+2 h x y+2 y^2-x+y-1=0\) is \(\operatorname{Tan}^{-1}(3 / 4)\) and \(h\) is a positive rational number, then the point of intersection of these two lines is

  1. A \((1,-1)\)
  2. B \(\left(\frac{-1}{9}, \frac{1}{9}\right)\)
  3. C \((-1,1)\)
  4. D \((3,2)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((-1,1)\)

Step-by-step Solution

Detailed explanation

\(\tan \theta = \frac{2 \sqrt{h^2 - AB}}{|A+B|}\) \(\frac{3}{4} = \frac{2 \sqrt{h^2 - (2)(2)}}{|2+2|}\) \(\frac{3}{4} = \frac{2 \sqrt{h^2 - 4}}{4}\) \(\sqrt{h^2 - 4} = \frac{3}{2}\) \(h^2 - 4 = \frac{9}{4}\) \(h^2 = \frac{25}{4} \implies h = \frac{5}{2}\) (since h is positive)…