TS EAMCET · Maths · Straight Lines
The line passing through \(\left(-1, \frac{\pi}{2}\right)\) and perpendicular to \(\sqrt{3} \sin \theta+2 \cos \theta=\frac{4}{r}\) is :
- A \(2=\sqrt{3} r \cos \theta-2 r \sin \theta\)
- B \(5=-2 \sqrt{3} r \sin \theta+4 r \cos \theta\)
- C \(2=\sqrt{3} r \cos \theta+2 r \sin \theta\)
- D \(5=2 \sqrt{3} r \sin \theta+4 r \cos \theta\)
Answer & Solution
Correct Answer
(A) \(2=\sqrt{3} r \cos \theta-2 r \sin \theta\)
Step-by-step Solution
Detailed explanation
Given, \(\sqrt{3} \sin \theta+2 \cos \theta=\frac{4}{r}\) ...(i) Any line perpendicular to Eq. (i) is \(\sqrt{3} \sin \left(\frac{\pi}{2}+\theta\right)+2 \cos \left(\frac{\pi}{2}+\theta\right)=\frac{k}{r}\) \(\sqrt{3} \cos \theta-2 \sin \theta=\frac{k}{r}\) It passes through…
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 condition \(f(x)=x^3+p x^2+q x+r(x \in R)\) to have no extreme value, isTS EAMCET 2007 Medium
- If the vector \(\mathbf{a}=3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) is the sum of two vectors \(\mathbf{a}_1\) and \(\mathbf{a}_2\), vector \(\mathbf{a}_1\) is parallel to \(\mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and vector \(\mathbf{a}_2\) is perpendicular to \(\mathbf{b}\), then \(\mathbf{a}_1=\)TS EAMCET 2019 Easy
- \(\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots . .\left(1+\frac{n^2}{n^2}\right)\right]^{1 / n}=\)TS EAMCET 2020 Hard
- Let \(a\) be maximum value of \((3 \cos \theta-4 \sin \theta)\) and \(\theta \neq \frac{n \pi}{2}\). If \(\alpha=a \sin ^2 \theta\). \(\cos ^3 \theta\) and \(\beta=a \sin ^3 \theta \cdot \cos ^2 \theta\), then \(\sqrt{\frac{\left(\alpha^2+\beta^2\right)^5}{(\alpha \beta)^4}}=\)TS EAMCET 2020 Easy
- The locus of the mid-points of the chords of the circle \(x^2+y^2=16\) which are tangents to the hyperbola \(9 x^2-16 y^2=144\) isTS EAMCET 2018 Medium
- If \(\mathrm{i}^2=-1\) then \((1+\sqrt{3} \mathrm{i})^{2022}-(\sqrt{3}-\mathrm{i})^{2022}=\)TS EAMCET 2023 Easy
More PYQs from TS EAMCET
- If all the letters of the word ACADEMICIAN are permuted in all possible ways then the number of permutations in which no two A's are together and all the consonants are together isTS EAMCET 2025 Hard
- \(\operatorname{coth}^{-1} 3+\tanh ^{-1} \frac{1}{3}-\operatorname{cosech}^{-1}(-\sqrt{3})=\)TS EAMCET 2018 Medium
- If \(\mathrm{L}_1\) is a line passing through the point \(\mathrm{P}(4,-3)\) and perpendicular to the line \(3 x-4 y+k=0\), then the distance of \(P\) from the line \(5 x-3 y-2=0\) measured along the line \(\mathrm{L}_1\) isTS EAMCET 2023 Easy
- 0.1 mole of \(\mathrm{NaCl}\) is dissolved in \(100 \mathrm{~g}\) of water. The mole fraction of \(\mathrm{NaCl}\) isTS EAMCET 2018 Easy
- If and denote energies at time and respectively, and and distance from some point at and respectively, then which of the following equations can be declared to be incorrect on dimensional grounds (A) (B) (C) (D)TS EAMCET 2022 Easy
- The cubic unit cell of a metal (molar mass \(=63.55 \mathrm{~g} \mathrm{~mol}^{-1}\) ) has an edge length of \(362 \mathrm{pm}\). Its density is \(8.92 \mathrm{~g} \mathrm{~cm}^{-3}\). The type of unit cell isTS EAMCET 2009 Easy