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
- A \((1,-1)\)
- B \(\left(\frac{-1}{9}, \frac{1}{9}\right)\)
- C \((-1,1)\)
- D \((3,2)\)
Answer & Solution
Correct Answer
(C) \((-1,1)\)
Step-by-step Solution
Detailed explanation
\(\tan \theta = \frac{2\sqrt{h^2 - ab}}{a+b}\) \(\frac{3}{4} = \frac{2\sqrt{h^2 - (2)(2)}}{2+2}\) \(\frac{3}{2} = \sqrt{h^2 - 4}\) \(\frac{9}{4} = h^2 - 4 \⇒ h^2 = \frac{25}{4} \⇒ h =…
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