TS EAMCET · Maths · Straight Lines
If the line joining the points \(A(b \cos \alpha, b \sin \alpha)\) and \(B(a \cos \beta, a \sin \beta)\) is extended to the point \(N(x, y)\) such that \(A N: N B=b: a\), then
- A \(x \cos \frac{\alpha-\beta}{2}+y \sin \frac{\alpha+\beta}{2}=0\)
- B \(x \cos \frac{\alpha-\beta}{2}+y \sin \frac{\alpha-\beta}{2}=0\)
- C \(x \cos \frac{\alpha+\beta}{2}+y \sin \frac{\alpha+\beta}{2}=0\)
- D \(x \cos \frac{\alpha+\beta}{2}+y \sin \frac{\alpha-\beta}{2}=0\)
Answer & Solution
Correct Answer
(C) \(x \cos \frac{\alpha+\beta}{2}+y \sin \frac{\alpha+\beta}{2}=0\)
Step-by-step Solution
Detailed explanation
Coordinate of \(N\) will be \( x=\frac{m_1 x_2-m_2 x_1}{m_1-m_2}, \quad y=\frac{m_1 y_2-m_2 y_1}{m_1-m_2} \) So, \( x=\frac{b \cdot a \cos \beta-a \cdot b \cos \alpha}{b-a}, \) \(\Rightarrow \quad y=\frac{b \cdot a \sin \beta-a \cdot b \sin \alpha}{b-a}\)…
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 \(A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\), then for all \(n \in N\)TS EAMCET 2018 Easy
- ForTS EAMCET 2021 Medium
- For integer \(k\), if the area of the triangle formed by the pair of lines \(S=3 x^2-2 k x y+y^2=0\) with the line \(L=2 x-y-6=0\) is 36 sq. units, then for the angle \(\theta\) between the lines \(S=0, \sin \theta=\)TS EAMCET 2020 Medium
- Let \(X\) be binomial variate with parameters \(n=6\) and \(p\). If \(4 P(X=4)=P(X=2)\), then \(p\) equalsTS EAMCET 2015 Easy
- If \(f:[-6,6] \rightarrow R\) is defined by \(f(x)=x^2-3\) for \(x \in R\), then \[ (f \circ f \circ f)(-1)+(f \circ f \circ f)(0)+(f \circ f \circ f)(1) \] is equal toTS EAMCET 2008 Hard
- If \(a, b, c, \neq 0\) and belong to the set to \(\{0,1,2\), \(3 \ldots \ldots, 9\}\), then \(\log _{10}\left(\frac{a+10 b+10^2 c}{10^{-4} a+10^{-3} b+10^{-2} c}\right)\) is equal toTS EAMCET 2005 Hard
More PYQs from TS EAMCET
- A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is \(0.9 \mathrm{~g} \mathrm{~cm}^{-3}\), the mass of the wooden cube isTS EAMCET 2024 Easy
- The probability distribution of a random variable \(X\) is given below.
Then the variance of \(X\) isTS EAMCET 2011 Easy - Which air pollutant is responsible for Bhopal gas tragedy?TS EAMCET 2011 Easy
- \(\int_0^{\pi / 4}[\sqrt{\tan x}+\sqrt{\cot x}] d x\) is equal toTS EAMCET 2016 Medium
- \(\int_0^4|| x-2|-x| d x=\)TS EAMCET 2022 Medium
- The local maximum value of the function isTS EAMCET 2022 Easy