WBJEE · Maths · Straight Lines
A straight line through the point of intersection of the lines \(x+2 y=4\) and \(2 x+y=4\) meets the coordinate axes at \(A\) and \(B\). The locus of the mid-point of \(A B\) is
- A \(3(x+y)=2 x\)
- B \(2(x+y)=3 x y\)
- C \(2(x+y)=x\)
- D \(x+y=3 x y\)
Answer & Solution
Correct Answer
(B) \(2(x+y)=3 x y\)
Step-by-step Solution
Detailed explanation
Given lines are, \[ x+2 y=4 \] and \(\quad 2 x+y=4\) Solving Eqs. (i) and (ii), we get \[ x=\frac{4}{3}, y=\frac{4}{3} \] Let \(\quad A B: \frac{x}{a}+\frac{y}{b}=1\) Meets \(x\) -axis at \(A\) and \(y\) -axis at \(B\). If the straight line (iii) passes through the point…
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 value of the integral \(\int_{-1}^{1}\left\{\frac{x^{2015}}{e^{\mid x \mid}\left(x^{2}+\cos x\right)}+\frac{1}{e^{\mid{x} \mid}}\right\} d x\) is equal toWBJEE 2019 Hard
- What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any questions?WBJEE 2021 Medium
- The number of solutions of \(2 \sin x+\cos x=3\) isWBJEE 2011 Easy
- The function \(f(x)=a \sin |x|+b e^{| x \mid} \quad\) is differentiable at \(x=0\) whenWBJEE 2014 Medium
- Let \(\mathrm{S}, \mathrm{T}, \mathrm{U}\) be three non-void sets and \(\mathrm{f}: \mathrm{S} \rightarrow \mathrm{T}, \mathrm{g}: \mathrm{T} \rightarrow \mathrm{U}\) and composed mapping \(\mathrm{gof}: \mathrm{S} \rightarrow U\) be defined. Let \(\mathrm{gof}\) be injective mapping. ThenWBJEE 2022 Medium
- Let \(P(2,-3), Q(-2,1)\) be the vertices of the \(\Delta P Q R .\) If the centroid of \(\Delta P Q R\) lies on the line \(2 x+3 y=1,\) then the locus of \(R\) isWBJEE 2012 Easy
More PYQs from WBJEE
- If \(x, y\) and \(z\) are greater than 1 , then the value of \(\left|\begin{array}{ccc}1 & \log _{x} y & \log _{x} z \\ \log _{y} x & 1 & \log _{y} z \\ \log _{z} x & \log _{z} y & 1\end{array}\right|\) isWBJEE 2016 Medium
- The solutions set of inequation \(\cos ^{-1} x < \sin ^{-1} x\) isWBJEE 2011 Easy
- A particle of mass \(M\) and charge \(q\) is at rest at the mid point between two other fixed similar charges each of magnitude \(Q\) placed a distance \(2 d\) apart. The system is collinear as shown in the figure. The particle is now displaced by a small amount \(x(x< < d)\) along the joining the two charges and is left to itself. It will now oscillate about the mean position with a time period \(\left(\varepsilon_{0}=\right.\) permittivity of free space)
WBJEE 2013 Hard - The light beams of intensities in the ratio of \(9: 1\) are allowed to interfere. What will be the ratio of the intensities of maxima and minima?WBJEE 2010 Easy
- If the equation \(\sin ^4 x-(p+2) \sin ^2 x-(p+3)=0\) has a solution, the \(p\) must lie in the intervalWBJEE 2025 Medium
- The value of the integral \(\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x\) isWBJEE 2025 Medium