SATHEE: Straight Line Question 250

Straight Line Question 250

Question: A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at points P and Q. as L varies the absolute minimum value of $ OP+OQ $ is (O is origin)

Options:

A) 28

B) 15

C) 18

D) 10

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Let the equation of the line L be $ y-2=m(x-8),m<0 $ Coordinates of P and Q are $ P( 8-\frac{2}{m},0 ) $ and $ Q(0,2-8m). $ So, $ OP+OQ=8-\frac{2}{m}+2-8m $ $ =10+\frac{2}{-m}+8(-m) $ $ \ge 10+2\sqrt{\frac{2}{-m}\times 8(-m)}\ge 18 $ absolute min. value of $ OP+OQ=18. $

BETA

sathee@iitk.ac.in

Media coverage of SATHEE

Play Store

App Store

The Ministry of Education has launched the SATHEE initiative in association with IIT Kanpur to provide free guidance for competitive exams. SATHEE offers a range of resources, including reference video lectures, mock tests, and other resources to support your preparation. Please note that participation in the SATHEE program does not guarantee clearing any exam or admission to any institute.

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 Question 250

Question: A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinate axes at points P and Q. as L varies the absolute minimum value of $ OP+OQ $ is (O is origin)

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

Menu