WBJEE · Maths · Straight Lines
If the three points \(A(1,6), B(3,-4)\) and \(C(x, y)\) are collinear then the equation satisfying by \(x\) and \(y\) is
- A \(5 x+y-11=0\)
- B \(5 x+13 y+5=0\)
- C \(5 x-13 y+5=0\)
- D \(13 x-5 y+5=0\)
Answer & Solution
Correct Answer
(A) \(5 x+y-11=0\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Hints: }\left|\begin{array}{ccc} 1 & 1 & 6 \\ 1 & 3 & -4 \\ 1 & x & y \end{array}\right|=0 \\ & \Rightarrow 1(3 y+4 x)-(y-6 x)+1(-4-18)=0 \Rightarrow 3 y+4 x-y+6 x-12=0 \\ & \Rightarrow 2 y+10 x-22=0 \\ & y+5 x=11 \end{aligned}\)
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 is a non-singular matrix of order \(5 \times 5\) and the sum of the elements of each row is 1 , then the sum of the elements of each row in \(\mathrm{P}^{-1}\) isWBJEE 2025 Medium
- The area bounded by the curves \(x=4-y^2\) and the \(Y\)-axis isWBJEE 2024 Easy
- In a triangle \(\mathrm{ABC}\) if \(\sin \mathrm{A} \sin \mathrm{B}=\frac{\mathrm{ab}}{\mathrm{c}^2}\), then the triangle isWBJEE 2009 Easy
- Let \(P\) be the foot of the perpendicular from focus \(S\) of hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) on the line \(b x-a y=0\) and let \(C\) be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of \(S P\) and \(C P\) isWBJEE 2017 Medium
- The value of \(\sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right), i=\sqrt{-1}\) isWBJEE 2016 Easy
- Let \(A=\left[\begin{array}{ccc}5 & 5 \alpha & \alpha \\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5\end{array}\right]\). If \(|\mathrm{A}|^2=25\), then \(|\alpha|\) equals toWBJEE 2025 Easy
More PYQs from WBJEE
- \(360 \mathrm{~cm}^3\) of a hydrocabon diffuses in 30 minutes, while under the same conditions \(360 \mathrm{~cm}^3\) of \(\mathrm{SO}_2\) gas diffuses in one hour. The molecular formula of the hydrocabon isWBJEE 2025 Medium
- The value of the integral \(\int_0^{\pi / 2} \sin ^5 x d x\) isWBJEE 2010 Medium
- The reduction potential of hydrogen half-cell will be negative ifWBJEE 2021 Medium
- Let \(P\) be the set of all non-singular matrices of order 3 over \(R\) and \(Q\) be the set of all orthogonal matrices of order 3 over \(R .\) Then,WBJEE 2017 Easy
- Let \(A\) and \(B\) are orthogonal matrices and \(\operatorname{det} A+\operatorname{det} B=0\). ThenWBJEE 2023 Hard
- If the tangent to \(y^{2}=4 a x\) at the point \(\left(a t^{2}, 2 a t\right)\) where \(|t|>1\) is a normal to \(x^{2}-y^{2}=a^{2}\) at the point \((a \sec \theta, a \tan \theta),\) thenWBJEE 2017 Medium