AP EAMCET · Maths · Straight Lines
Suppose \(P\) and \(Q\) lie on \(3 x+4 y-4=0\) and \(5 x-y-4=0\) respectively. If the mid-point of \(P Q\) is \((1,5)\), then the slope of the line passing through \(P\) and \(Q\) is
- A \(\frac{83}{35}\)
- B \(\frac{65}{35}\)
- C \(\frac{-3}{4}\)
- D \(\frac{3}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{83}{35}\)
Step-by-step Solution
Detailed explanation
Let the line \(P Q\) be. \(y-5=m(x-1)\) ...(i) Substituting \(y=m x+5-m\) in the equation \(5 x-y-4=0\) We have, \(.5 x-m x-5+m-4=0\) \(\Rightarrow \quad(5-m) x+m-9=0\) Therefore, \(x=\frac{9-m}{5-m}\) and \(y=m\left(\frac{9-m}{5-m}\right)+5-m\) \(=\frac{25-m}{5-m}\) Here,…
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 \((2+i)\) is a root of the equation \(x^3-5 x^2+9 x-5=0\), then the other roots areAP EAMCET 2020 Medium
- A variable plane passes through a fixed point \((\alpha, \beta, \gamma)\) and meets the coordinate axes in \(A, B\) and \(C\). Let \(P_1, P_2\) and \(P_3\) be the planes passing through \(A, B, C\) and parallel to the coordinate planes \(Y Z, Z X, X Y\) respectively. Then, the locus of the point of intersection of the planes \(P_1, P_2\) and \(P_3\) isAP EAMCET 2018 Medium
- If the axes are rotated through an angle \(45^{\circ}\) in the positive direction without changing the origin, then the co-ordinates of the point \((\sqrt{2}, 4)\) in the old system areAP EAMCET 2002 Hard
- For \(x\) and \(y\) satisfying \(|x|+|y|=|x-3|+|y-2|\), which of the following is correct?AP EAMCET 2022 Medium
- If \(\frac{2+3 i \sin \theta}{1-2 i \sin \theta}\) is purely imaginary, then \(\cos ^2 \theta=\)AP EAMCET 2017 Easy
- Let \(A=\left[\begin{array}{cc}1 & 2 \\ -2 & 1\end{array}\right]\) and \(B^{-1}=\left[\begin{array}{ll}1 & 1 \\ 0 & 2\end{array}\right]\). If \(\left(A B^{-1}\right)^{-1}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\), then \(2 b+5 c+10 d=\)AP EAMCET 2022 Easy
More PYQs from AP EAMCET
- \(\mathrm{C}-\mathrm{Cl}\) bond lengths (in pm) in haloarene and haloalkane are respectivelyAP EAMCET 2017 Medium
- In an oscillating \(L C\) circuit, the maximum charge on the capacitor is \(Q\). The charge on the capacitor when the energy is stored equally between the electric and magnetic fields isAP EAMCET 2019 Easy
- Consider the following lists.
\(\begin{array}{ll} \text { List I } & \text { List II } \\ \hline \text { (A) } f(x)=\frac{|x+2|}{x+2}, x \neq-2 & \text { 1. }\left[\frac{1}{3}, 1\right] \\ \hline \text { (B) } g(x)=\mid[x \mid x \in R & \text { 2. } Z \\ \hline \text { (C) } h(x)=|x-[x]|, x \in R & \text { 3. } W \\ \hline \text { (D) } f(x)=\frac{1}{2-\sin 3 x}, x \in R & \text { 4. }[0,1) \\ \hline & \text { 5. }\{-1,1\} \end{array}\)AP EAMCET 2019 Medium - The number of linear and crosslinked polymers in the following respectively are
Novolac, Nylon 6,6, Bakelite, PVC, melamineAP EAMCET 2025 Medium - \(\int \sec \left(x-\frac{\pi}{3}\right) \sec \left(x+\frac{\pi}{6}\right) d x=\)AP EAMCET 2025 Medium
- Which of the following form an ideal sơlution?
I. Chloroethane and bromoethane
II. Benzene and toluene
III. \(n\)-hexane and \(n\)-heptane
IV. Phenol and anilineAP EAMCET 2022 Easy