Total Price: R

There are no items in this cart.
Continue Shopping

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
My all india rank is 344672. i'm a sc candidate. my sc rank is 19369. is there any chance for me to get admission in any nits or iiits? plz replyyy fasttt..
Is bit tough to get in IITs and NITs for your rank, better try for deemed ones for good branches
Avinash 20 hours ago
With the rank that you have mentioned, it does not seem to be possible, but due to your category, it may perhaps be possible....and you should wait for the last rounds of counselling too,...
-21 minutes ago
i am expecting 190-200 jee main paper 2 and scored 94.45 in tamilnadu board exam. can i get architecture spa and nits?
Hi.. As per the scores you are describing, since your percentage is good, there are chances that you can get architecture in NITs. You can also try for other branches in other NITs also....
Sakshi 15 days ago
No its difficult to get seat in SPA or NIT as you are very far from expected cutoff range.
Avinash 15 days ago
Its difficult in getting selected in top university. there are many universities which provide you excellent placement,top infrastructure,desired course The top universities 1 BITS, Pilani...
abhinaipadachuru 14 days ago
I have got 5957 rank in jee advance 2015. What is the best according to you I can get??
I have no personal intrests..
Annu Purohit 15 hours ago
Did you check the cutoff list or the results of counselling rounds? If not, then I suggest you to do it on priority basis and which branch may me allotted to you, it all depends on the...
1 hour ago
i will appear in iitjee in 2011 . how should i prepare for it ?
Dear rounik Fitst I will suggest you to join any coaching classes.Because as you are preapearing for IIT JEE then you will face a tough comptition. coaching classes can guide in a better...
Badiuddin askIITians.ismu Expert 5 years ago
Where is the MANIPAL UNIVERSITY ENTRACNE MBBS previous years’ papers with solution? Please give me the link. Thank you Pushkarni
This is the link: Or else you can buy this book: 14 Years' Solved Papers Manipal UGET (MAHE) Medical by Arihant Experts.
Raheema Javed one month ago
What is OSI Reference Model ??
The Open System Interconnection reference model was created by the International Organizaiton for Standardization (ISO) to provide a model that network vendors could follow when developing...
Deepak Patra 6 years ago
View all Questions »