WBJEE · Maths · Straight Lines
The area of the triangle formed by the intersection of a line parallel to \(X\) -axis and passing through \(P(h, k),\) with the lines \(y=x\) and \(x+y=2\) is \(h^{2}\). The locus of the point \(P\) is
- A \(x=y-1\)
- B \(x=-(y-1)\)
- C \(x=1+y\)
- D \(x=-(1+y)\)
Answer & Solution
Correct Answer
(B) \(x=-(y-1)\)
Step-by-step Solution
Detailed explanation
Given, ar \((\Delta A B C)=h^{2}\) \(\Rightarrow \quad \frac{1}{2}\left|\begin{array}{ccc}1 & 1 & 1 \\ k & k & 1 \\ 2-k & k & 1\end{array}\right|=\pm h^{2}\) \(\Rightarrow 1(k-k)-1(k-2+k)+1\left(k^{2}-2 k+k^{2}\right)=\pm 2 h^{2}\)…
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
- Let \(\omega(\neq 1)\) be a cubic root of unity. Then the minimum value of the set \(\left\{\left|a+b \omega+c \omega^2\right|^2 ; a, b, c\right.\) are distinct non-zero integers} equalsWBJEE 2025 Hard
- \(\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x\)WBJEE 2011 Hard
- The set of points of discontinuity of the function \(f(x)=x-[x], x \in \mathbb{R}\) isWBJEE 2025 Easy
- A hyperbola, having the transverse axis of length \(2 \sin \theta\) is confocal with the ellipse \(3 x^{2}+4 y^{2}=12\). It equation isWBJEE 2018 Medium
- If four distinct points \((2 k, 3 k),(2,0),(0,3)\) (0,0) lie on a circle, thenWBJEE 2012 Medium
- Suppose that \(f(x)\) is a differentiable function such that \(f^{\prime}(x)\) is continuous, \(f^{\prime}(0)=1\) and \(f^{\prime \prime}(0)\) does not exist. Let \(g(x)=x f^{\prime}(x) .\) Then,WBJEE 2014 Medium
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
- Match the flame colours of the alkaline earth metal salts in the Bunsen burner
\(\begin{array}{l|l}
\hline \text{A. Caicium} & \text{p. Brick red} \\
\hline \text{B. Strontium} & \text{q. Apple green} \\
\hline \text{C. Barium} & \text{r. Crimson} \\
\hline
\end{array}\)WBJEE 2015 Easy -
In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas. If \(\Delta \mathrm{U}_{1}, \Delta \mathrm{U}_{2}, \Delta \mathrm{U}_{3}\) be the changes in internal energy in these processes respectively, thenWBJEE 2021 Easy - If \(\left|\begin{array}{lll}x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3}\end{array}\right|=(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\), thenWBJEE 2024 Easy
- Let \(f\) be a strictly decreasing function defined on \(\mathbb{R}\) such that \(f(x) > 0, \forall x \in \mathbb{R}\). Let \(\frac{x^2}{f\left(a^2+5 a+3\right)}+\frac{y^2}{f(a+15)}=1\) be an ellipse with major axis along the \(y\)-axis. The value of ' \(a\) ' can lie in the interval (s)WBJEE 2023 Medium
- The ease of hydrolysis in the compounds \(\mathrm{CH}_{3} \mathrm{COCl}(\mathrm{I}), \mathrm{CH}_{3}-\mathrm{CO}-\mathrm{O}-\mathrm{COCH}_{3}(\mathrm{II})\)
\(\mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(\mathrm{III})\) and \(\mathrm{CH}_{3} \mathrm{CONH}_{2}\) (IV) is of
the orderWBJEE 2018 Medium