WBJEE · Maths · Straight Lines
A moving line intersects the lines \(x+y=0\) and \(x-y=0\) at the points A, B respectively such that the area of the triangle with vertices \((0,0), A \& B\) has a constant area \(C\). The locus of the mid-point \(A B\) is given by the equation
- A \(\left(x^{2}+y^{2}\right)^{2}=C^{2}\)
- B \(\left(x^{2}-y^{2}\right)^{2}=C^{2}\)
- C \((x+y)^{2}=C^{2}\)
- D \((x-y)^{2}=C^{2}\)
Answer & Solution
Correct Answer
(B) \(\left(x^{2}-y^{2}\right)^{2}=C^{2}\)
Step-by-step Solution
Detailed explanation
Let mid point of \(\mathrm{AB}=(\mathrm{h}, \mathrm{k})\) Let, \(A=(\alpha,-\alpha), B=(\beta, \beta)\) \(\therefore \beta+\alpha=2 \mathrm{~h}, \quad \beta-\alpha=2 \mathrm{k}\) Area…
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 expression \(2^{4 n}-15 n-1\), where \(n \in \mathbb{N}\) (the set of natural numbers) is divisible byWBJEE 2025 Medium
- Let \(y=f(x)\) be any curve on the \(X-Y\) plane \& \(P\) be a point on the curve. Let \(C\) be a fixed point not on the curve. The length \(P C\) is either a maximum or a minimum, thenWBJEE 2024 Medium
- If \(f(x)=e^{x}(x-2)^{2},\) thenWBJEE 2013 Easy
- The area of the region enclosed between parabola \(y^{2}=x\) and the line \(y=m x\) is \(\frac{1}{48}\)
Then, the value of \(m\) isWBJEE 2013 Medium - The limit of \(\left\{\frac{1}{x} \sqrt{1+x}-\sqrt{1+\frac{1}{x^{2}}}\right\}\) as \(x \rightarrow 0\)WBJEE 2013 Easy
- A is a set containing n elements. \(P\) and \(Q\) are two subsets of \(A\). Then the number of ways of choosing \(P\) and \(Q\) so that \(P \cap Q=\varphi\) isWBJEE 2022 Easy
More PYQs from WBJEE
- If \(\lim _{x \rightarrow 0} \frac{2 a \sin x-\sin 2 x}{\tan ^{3} x}\) exists and is equal to 1 then the value of \(a\) isWBJEE 2014 Easy
- If one of the diameters of the curve \(x^{2}+y^{2}-4 x-6 y+9=0\) is a chord of a circle with centre \((1,1),\) the radius of this circle isWBJEE 2017 Easy
- Of the following acids the one which has the capability to form complex compound and also possesses oxidizing and reducing properties is :WBJEE 2009 Easy
- Let \(A\) and \(B\) be two square matrices of order 3 and \(A B=O_{3}\), where \(O_{3}\) denotes the null matrix of order 3. Then,WBJEE 2019 Easy
- \[
\text { At identical temperature and pressure, the rate of diffusion of hydrogen gas is } 3 \sqrt{3} \text { times that }
\]
of a hydrocarbon having molecular formula \(\mathrm{C}_{\mathrm{n}} \mathrm{H}_{2 \mathrm{n}-2}\). What is the value of ' \(n\) '?WBJEE 2010 Hard - How many electrons are needed to reduce \(\mathrm{N}_2\) to \(\mathrm{NH}_3\) ?WBJEE 2025 Easy