AP EAMCET · Maths · Pair of Lines
Which among the following represents the combined equation of a pair of lines through point \((1,0)\) and parallel to the lines represented by \(2 x^2-x y-y^2=0\).
- A \(2 x^2-x y-2 y^2+4 x-y=6\)
- B \(2 x^2-x y-y^2-4 x+y+2=0\)
- C \(2 x^2-x y-2 y^2-4 x+y+2=0\)
- D \(2 x^2-x y-y^2-4 x-y=2\)
Answer & Solution
Correct Answer
(B) \(2 x^2-x y-y^2-4 x+y+2=0\)
Step-by-step Solution
Detailed explanation
Given line, \(2 x^2-x y-y^2=0...(i)\) \(\begin{aligned} \Rightarrow \quad 2 x^2-2 x y+x y-y^2 & =0 \\ 2 x(x-y)+y(x-y) & =0 \\ (2 x+y)(x-y) & =0\end{aligned}\) Since, we have given that combined equation of the pair is parallel to \(2 x^2-x y-y^2=0\) So, combined equation will be…
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 \(P\) and \(Q\) are two non-zero square matrices of the same order such that the product \(P Q=0\), then ........AP EAMCET 2020 Medium
- If the product of the perpendicular distances from any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) to its asymptotes is 6 and eccentricity of the hyperbola is \(\sqrt{3}\), then the length of the conjugate axis of the hyperbola isAP EAMCET 2022 Medium
- Let \((\vec{a}, \vec{b})\) denote the angle between vectors \(\vec{a}\) and \(\vec{b}\). If \(\vec{a}=2 \hat{i}+3 \hat{j}+6 \hat{k}, \vec{a} \cdot \vec{b}=4\) and \((\vec{a}, \vec{b})=\cos ^{-1}\left(\frac{4}{21}\right)\), then \(\overline{\mathrm{a}}+\overline{\mathrm{b}}=\)AP EAMCET 2023 Easy
- If \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=7 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) are two vectors and \((2 \vec{a}-3 \vec{b}) \times(4 \vec{a}+\vec{b})=x \hat{i}+y \hat{j}+z \hat{k}\), then \(x+y+z=\)AP EAMCET 2023 Easy
- Let \(M\) and \(m\) respectively denote the maximum and the minimum values of \([f(\theta)]^2\), where \(f(\theta)=\sqrt{a^2 \cos ^2 \theta+b^2 \sin ^2 \theta}\) \(+\sqrt{a^2 \sin ^2 \theta+b^2 \cos ^2 \theta}\). Then \(M-m=\)AP EAMCET 2019 Medium
- Let \(A=\left[\begin{array}{rrr}-1 & -2 & -3 \\ 3 & 4 & 5 \\ 4 & 5 & 6\end{array}\right], B=\left[\begin{array}{cr}1 & -2 \\ -1 & 2\end{array}\right] \quad\) and \(C=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]\), if \(a, b\) and \(c\) respectively, denote the ranks of \(A, B\) and \(C\), then the correct order of these number isAP EAMCET 2012 Easy
More PYQs from AP EAMCET
- The resistance between points A and C in the given network is
AP EAMCET 2024 Easy - The interval in which the curve represented by \(f(x)=2 x+\log \left(\frac{x}{2+x}\right)\) is increasing isAP EAMCET 2025 Medium
- Suppose \(A(2,3)\) and \(B\) are the points of intersections of two circles. The points \(P\) lying on one circle and \(Q\) lying on the other circle are such that \(B P\) and \(B Q\) constitute the diameters of the circles. If the slopes of the radical axis and \(P Q\) are \(3 / 4\) and \(a / b\) respectively, then the value of \(3 a+4 b\) isAP EAMCET 2022 Medium
- Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, then the probability that atleast one of them is a face card isAP EAMCET 2025 Medium
- Which of the following statements regarding centre of mass is NOT true?AP EAMCET 2023 Easy
- If the circle \(x^2+y^2+8 x-4 y+c=0\) touches the circle \(x^2+y^2+2 x+4 y-11=0\) externally and cuts the circle \(x^2+y^2-6 x+8 y+k=0\) orthogonally, then \(k\) is equal toAP EAMCET 2011 Hard