SATHEE: Straight Line and Pair of Straight Lines 1 Question 18

Straight Line and Pair of Straight Lines 1 Question 18

18. A straight line through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$ . If $O$ is the origin and the rectangle $O P R Q$ is completed, then the locus of $R$ is

(2018 Main)

(a) $3 x + 2 y = 6$

(b) $2 x + 3 y = x y$

(c) $3 x + 2 y = x y$

(d) $3 x + 2 y = 6 x y$

Show Answer

Solution:

Equation of line $P Q$ is $\frac{x}{α} + \frac{y}{β} = 1$

Since this line is passes through fixed point $(2, 3)$ .

$∴ \frac{2}{α} + \frac{3}{β} = 1$

$∴$ Locus of $R$ is

$2 β + 3 α = α β$

i.e.

$2 y + 3 x = x y \Rightarrow 3 x + 2 y = x y$

Privacy Policy

Powered by Prutor@IITK

sathee@iitk.ac.in

Media coverage of SATHEE

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 1 Question 18

18. A straight line through a fixed point (2,3) intersects the coordinate axes at distinct points P and Q. If O is the origin and the rectangle OPRQ is completed, then the locus of R is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

18. A straight line through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$ . If $O$ is the origin and the rectangle $O P R Q$ is completed, then the locus of $R$ is