AP EAMCET · Maths · Pair of Lines
If the slope of one of the lines in the pair of lines \(8 x^2+a x y+y^2=0\) is thrice the slope of the second line, then \(a=\)
- A \(8 \sqrt{\frac{2}{3}}\)
- B \(6\)
- C \(16 \sqrt{2}\)
- D \(3 \frac{\sqrt{2}}{5}\)
Answer & Solution
Correct Answer
(A) \(8 \sqrt{\frac{2}{3}}\)
Step-by-step Solution
Detailed explanation
\(8 x^2+a x y+y^2=0\) Let \(m_1\) and \(m_2\) be two slopes Since given equation is homogeneous \(\Rightarrow m_1+m_2=\frac{-a}{1}\) and \(m_1 m_2=8 ;\) Since \(m_1=3 m_2\) \(\therefore 3 m_2+m_2=-\mathrm{a} \Rightarrow 4 m_2=-\mathrm{a}\) ...(i) and…
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
- \(\cosh \alpha+\sinh \alpha=\mathrm{e}^3\) and \(\sinh \mathrm{x}=\frac{\alpha}{\alpha+1}\), then \(\tanh \mathrm{x}=\)AP EAMCET 2023 Hard
- If the latusrectum of an ellipse subtends a right angle at the centre of that ellipse, then the eccentricity of that ellipse isAP EAMCET 2018 Easy
- If the roots of the equation \(x^3+a x^2+b x+c=0\) are in arithmetic progression, thenAP EAMCET 2024 Easy
- Let be the origin and be a point which is at a distance of units from the origin. If the direction ratios of are , then the coordinates of areAP EAMCET 2021 Medium
- If \(f(x)=\left\{\begin{array}{cc}\frac{2 x e^{\frac{1}{2 x}}-3 x e^{\frac{-1}{2 x}}}{e^{\frac{1}{2 x}}+4 e^{\frac{-1}{2 x}}} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right.\)
is a real valued function thenAP EAMCET 2024 Medium - If \(\lim _{x \rightarrow \infty}\left\{\frac{x^3+1}{x^2+1}-(\alpha x+\beta)\right\}\) exists and equal to 2 , then the ordered pair \((\alpha, \beta)\) of real numbers isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- If \(\mathrm{X}, \mathrm{Y}\) and Z are the sizes of the emitter, base and collector of a transistor respectively, thenAP EAMCET 2025 Easy
- Let and be three positive real numbers such that the sum of any two of them is greater than the third. All the values of such that the roots of the equation are real, are given byAP EAMCET 2018 Medium
- What is the functional group present in serine, an aminoacid in addition to \(-\mathrm{NH}_2\) and \(-\mathrm{COOH}\) groups?AP EAMCET 2022 Easy
- \(\tan x+\frac{\cos x}{1+\sin x}=\)AP EAMCET 2022 Medium
- If two distinct points lying at a unit distance from \(4 \mathrm{x}+3 \mathrm{y}-10=0\) and passing through \(\mathrm{x}+\mathrm{y}=4\) are separated by a distance \(\mathrm{d}\), then the value of \(\mathrm{d}\) isAP EAMCET 2022 Medium
- The correct decreasing order of basic strength of \(\mathrm{H}_2 \mathrm{O}, \mathrm{NH}_3, \mathrm{OH}^{-}, \mathrm{NH}_2^{-}\)isAP EAMCET 2020 Easy