TS EAMCET · Maths · Pair of Lines
Let the line \(\mathrm{L}_1\) passing through the point of intersection of the lines \(2 x+3 y-5=0\) and \(4 x-5 y+7=0\) divide the line segment joining the points \((2,3)\) and \((1,-1)\) in the ratio \(2: 1\). If the equation of \(L_1\) is \(a x+b y=1\), then \(33(a-b)=\)
- A \(-1\)
- B \(0\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
Equation of line passing through point of intersection of \(L=0\) and \(l=0\) is \(L+\lambda l=0\) \[ \begin{aligned} & \Rightarrow(2 x+3 y-5)+\lambda(4 x-5 y+7)=0 \\ & L_1:(2+4 \lambda) x+(3-5 \lambda) y+(7 \lambda-5)=0 \end{aligned} \] \(\because L_1\) divides the line joining…
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 \(f:[2, \infty) \rightarrow \mathbb{R}\) is defined by \(f(x)=x^2-4 x+5\), then the range of \(f\) isTS EAMCET 2023 Easy
- If is an interior point of the curve then lies inTS EAMCET 2021 Easy
- If \(f(x)=\cosh ^1\left(\frac{1-x}{1+x}\right)\) is well defined, then \(f^{\prime}(x)=\)TS EAMCET 2019 Medium
- The co-ordinate axes are rotated through an angle \(135^{\circ}\). If the co-ordinates of a point \(P\) in the new system are known to be \((4,-3)\), then the co-ordinates of \(P\) in the original system areTS EAMCET 2003 Medium
- The probability of getting qualified in IITJEE and EAMCET by a student are respectively \(\frac{1}{5}\) and \(\frac{3}{5}\). The probability that the student gets qualified for atleast one of these test, isTS EAMCET 2002 Medium
- Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}x^2-4 x+3, & \text { if } x < 2 \ x-3, & \text { if } x \geq 2\end{array}\right.\) Then the number of real numbers \(x\) for which \(f(x)=8\) isTS EAMCET 2023 Easy
More PYQs from TS EAMCET
- If the vectors \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathrm{c}=x \hat{\mathbf{i}}+(x-2) \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are coplanar, then \(x=\)TS EAMCET 2017 Medium
- The hybridisation of central atom of isTS EAMCET 2021 Medium
- Let A and B be two events in a random experiment. If \(\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{B}})=0.1\), \(\mathrm{P}(\overline{\mathrm{A}} \cap \mathrm{B})=0.2\) and \(\mathrm{P}(\mathrm{B})=0.5\) then \(\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})=\)TS EAMCET 2025 Medium
- If the tangent and the normal drawn to the curve \(x y^2+x^2 y=12\) at the point \((1,3)\) meet the X -axis in T and N respectively, then \(\mathrm{TN}=\)TS EAMCET 2025 Medium
- Which one of the following statements is "not correct" about cationic detergents?TS EAMCET 2020 Medium
- If \(f: R /\{0\} \rightarrow R\) is such that \(2 f(x)+f\left(\frac{1}{x}\right)=4 x\) and \(S=\{x \in R: f(x)=f(-x)\}\), then the number of elements in \(S\) isTS EAMCET 2021 Easy