SATHEE: Straight Line and Pair of Straight Lines 3 Question 7

Straight Line and Pair of Straight Lines 3 Question 7

8. Three lines $p x + q y + r = 0, q x + r y + p = 0$ and $r x + p y + q = 0$ are concurrent, if

(1985, 2M)

(a) $p + q + r = 0$

(b) $p^{2} + q^{2} + r^{2} = p r + r q$

(d) None of these

Match the Columns

Match the conditions/expressions in Column I with statement in Column II.

Show Answer

Answer:

Correct Answer: 8. $(a, c)$

Solution:

Given lines $p x + q y + r = 0, q x + r y + p = 0$ and $r x + p y + q = 0$ are concurrent.

$∴ | \begin{array}{ccc} p & q & r q & r & p r & p & q \end{array} | = 0$

Applying $R_{1} \to R_{1} + R_{2} + R_{3}$ and taking common from $R_{1}$

$\begin{array}{rr} (p + q + r) | \begin{array}{lll} 1 & 1 & 1 \\ q & r & p \\ r & p & q \end{array} | = 0 \\ \Rightarrow & (p + q + r) (p^{2} + q^{2} + r^{2} - p q - q r - p r) = 0 \\ \Rightarrow & p^{3} + q^{3} + r^{3} - 3 p q r = 0 \end{array}$

Therefore, (a) and (c) are the answers.

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Straight Line and Pair of Straight Lines 3 Question 7

8. Three lines px+qy+r=0,qx+ry+p=0 and rx+py+q=0 are concurrent, if

Match the Columns

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

8. Three lines $p x + q y + r = 0, q x + r y + p = 0$ and $r x + p y + q = 0$ are concurrent, if