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
\(\tan \theta = \frac{2 \sqrt{h^2 - AB}}{|A+B|}\) \(\frac{3}{4} = \frac{2 \sqrt{h^2 - (2)(2)}}{|2+2|}\) \(\frac{3}{4} = \frac{2 \sqrt{h^2 - 4}}{4}\) \(\sqrt{h^2 - 4} = \frac{3}{2}\) \(h^2 - 4 = \frac{9}{4}\) \(h^2 = \frac{25}{4} \implies h = \frac{5}{2}\) (since h is positive)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The perpendicular distance from the point \(3 \bar{i}-2 \bar{j}+\bar{k}\) to the line joining the points \(\bar{i}-3 \bar{j}+5 \bar{k}\) and \(2 \bar{i}+\bar{j}-4 \bar{k}\) isAP EAMCET 2018 Easy
- The equation of the hyperbola with focus \((1,2), e=\sqrt{3}\) and directrix \(2 x+y=1\) is given byAP EAMCET 2020 Hard
- If a set \(A\) has 5 elements, then the number of ways of selecting two subsets \(P\) and \(Q\) from \(A\) such that \(P\) and \(Q\) are mutually disjoint, isAP EAMCET 2016 Easy
- If both the roots of the equation \(x^2-6 a x+2-2 a+9 a^2=0\) exceeds 3 , thenAP EAMCET 2024 Easy
- If \(\frac{x+1}{(x-1)^2\left(x^2+1\right)}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{C x+D}{x^2+1}\), then \(\sqrt{3 A^2+4 D^2+5 C^2+B^2}=\)AP EAMCET 2025 Medium
- If \(\left|z+\frac{2}{z}\right|=2\), then the maximum value of \(|z|\) isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- If \(f(x)=|x-1|+|x-2|+|x-3|, 2 < x < 3\), then \(f\) isAP EAMCET 2016 Easy
- Which of the following is a favourable factor for cation formation?AP EAMCET 2004 Easy
- Two statements are given below
Statement I: Chlorobenzene on nitration gives 1-chloro4-nitrobenzene as major product
Statement II: Chlorobenzene undergoes nitration slowly than benzene
Identify the correct answerAP EAMCET 2023 Medium - If \(b>a\), then \(\int_a^b \frac{d x}{\sqrt{(x-a)(b-x)}}\) is equal toAP EAMCET 2021 Hard
- If , thenAP EAMCET 2022 Hard
- One mole of 2-methylbuta-1, 3-diene on ozonolysis givesAP EAMCET 2022 Easy