let (h,k) be a fixed point where h,k>0.a straight line passing through this point cuts the positive direction of coordinate axes at points P and Q.find the minimum area of the triangle OPQ

4 years ago


Answers : (1)


Hi Rahul,

lets take the equation of line to be x/a + y/b = 1 where line intersects x axia at ( a, 0 ) and y axis at (0,b)

Since line passes thru (h,k) therefore h/a + k/b = 1. ------- (1)

A = area of triangle OPQ = 1/2 * a*b

from eqn (1)

A = 1/2 * b * hb / ( b- K ) ( putting value of a from (1) into A )

 = 1/2*b2h/(b - k)

to calculate min value of A, dA/db = 1/2 * h * ( b2 - 2bk ) / ( b-k )2

dA / db = 0 when b2 - 2bk = 0

or b -2k = 0

or b = 2k

At this value of b = 2k , the d2A / db2 is positive that is Minimum of A occurs at this value.

Putting in (1) a = 2h

Thus Minimum value of A occurs when a = 2h and b = 2k

Hence Min(A) = 1/2 * a * b = 1/2 * 2h * 2k = 2hk

Thus Minimum area of traingle OPQ is 2hk.

Please feel free to ask as many questions you have.





4 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details
Respected Sir/Madam, My question is regarding the enrolment procedure in the IIT’s. The question arised after i came to know about my elder sister who faced the problem. The question is as...
No, you can’t continue with the course alotte time around. That is why they ask you to fill the choice sheet carefully.If you are slide up then you have to continue with the new branch...
Aziz Alam 2 months ago
Sir, -How rank is decided in jee advanced? -Is it decided only on marks that we get in jee advanced paper?
It’s decided solely on the basis of the marks you secure on the JEE Advanced paper. Thanks & Regards Aziz Alam IIT Roorkee askIITians
Aziz Alam 2 months ago
I want to learn calculus from basics so which book should i use to master in calculus???
Hello Anup, If you want to learn the calculus from basics, then you should follow Arihant – Differential Calculus Arihant – Integral Calculus IA Maron All the three books are...
Jitender Singh 2 months ago
sir im arjit maine 2014 ki mp board preeksha 72% se pass ki hai main medical line main jana chahta hoo please give some idea
Hi Arjit Congratulations for passing your board exam. To go into medical line, you need to sit for Medical Entrance Exams that are conducted all over India (such as AIMPT, AIMS) and also by...
Sumreet Johar one month ago
how to balance between the studies for iit-jee and other all exams with it
Dear Shweta, Syllabus of IIT-JEE is more or less the same as other entrance exams. Other exams like AIEEE, BITSAT include several extra chapters to the IIT JEE syllabus. So if your...
Askiitians Expert Himanshu Geed - IIT Delhi 4 years ago
Dear shweta To balance between IIT JEE and all other exam ,you need not to make extra effort.because almost all the exam have same syllabus.only in few exam you will see few more chapters....
Badiuddin askIITians.ismu Expert 4 years ago
Please suggest online learning resource for online chemistry?
Here are some of the suggested ones: chemwiki, chemguide, chemcollective, http://chemistry-teaching-resources.com/Welcome.html
Sumreet Johar 2 months ago
View all Questions »