AP EAMCET · Maths · Pair of Lines
If \(x^2+\alpha y^2+2 \beta y=a^2\) represents a pair of perpendicular lines, then \(\beta\) equals to
- A \(4 a\)
- B \(a\)
- C \(2a\)
- D \(3a\)
Answer & Solution
Correct Answer
(B) \(a\)
Step-by-step Solution
Detailed explanation
Let given line be \[ x^2+\alpha y^2+2 \beta y-a^2=0 \] Here, \(a=1, b=\alpha, h=0, g=0, f=\beta, c=-a^2\) Condition for perpendicular line \(a+b=0\) \[ \therefore \quad 1+\alpha=0 \Rightarrow \alpha=-1 \] Condition of pair of lines…
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
- If \(\alpha_1, \alpha_2, \alpha_3, \alpha_4, \alpha_5\) are the roots of \(x^5-5 x^4+9 x^3-9 x^2\) \(+5 x-1=0\) then \(\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}=\)AP EAMCET 2024 Hard
- \(\left|\begin{array}{lll}24 & 25 & 26 \\ 25 & 26 & 27 \\ 26 & 27 & 27\end{array}\right|\) is equal toAP EAMCET 2011 Easy
- If four points are taken on each of three parallel lines in a plane, then the maximum number of triangles formed with these points isAP EAMCET 2018 Hard
- If \(\quad f: R \rightarrow R \quad\) is defined by \(f(x)=[x-3]+|x-4|\) for \(x \in R\), then \(\lim _{x \rightarrow 3^{-}} f(x)\) is equal toAP EAMCET 2008 Medium
- If the area of a square is 575 square units, then the approximate value of its side isAP EAMCET 2025 Easy
- If is defined by , where and is such that then the value of isAP EAMCET 2018 Easy
More PYQs from AP EAMCET
- \(\int \frac{x+\sin x}{1+\cos x} d x\) is equal toAP EAMCET 2021 Medium
- In hydrogen spectrum, the shortest wavelengths of Lyman and Balmer series are \(\lambda_1\) and \(\lambda_2\) respectively. The Rydberg constant of hydrogen isAP EAMCET 2023 Hard
- Observe the following solutions
I. Black coffee
II. \(0.2 \mathrm{M} \mathrm{NaOH}\)
III. Lemon juice
IV. Lime water
V. Human Saliva
VI. Tomato juice
The number of solutions with \(\mathrm{pH}\) less than 7 isAP EAMCET 2023 Easy - Which of the following reactions of \(\mathrm{KMnO}_4\) occurs in acidic medium?AP EAMCET 2024 Medium
- Ionosphere acts as a reflector for the frequency range ofAP EAMCET 2025 Easy
- A hyperbola passes through the point \(\mathrm{P}(\sqrt{2}, \sqrt{3})\) and has foci at \(( \pm 2,0)\). Then the point that lies on the tangent drawn to this hyperbola at P isAP EAMCET 2025 Medium