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

Share

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.


Puneet


 


 


 

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
Vouchers
To Win!!!
Click Here for details
I’m getting 5 years dual degree course M5213 in IIT Madras...There’s a doubt whether it is the core civil engineering branch or just infrastructural civil engineering?
 
 
It would be definitely infrastructural civil engineerin. It would be of 5 year integrated programme for which four and half year comprehensed on thetheory along with practical approach and...
  img
Saurabh Kumar 15 days ago
how to solve swimmer and river problems
 
 
Use the concept of relative velocity to solve the swimmer and river problems. If you know how to use relative velocity concept then those questions are very easy. So first understand...
  img
Ramreddy one month ago
 
Hii You ahve to consider speeds of boat and river After that consider two cases of Upstream and Downstream with values “X-Y” and “X+ Y” respectively thanks....
  img
Sourabh Singh one month ago
what does the transaction details mean in the declaration form
 
 
Hello Dear student, You have to give the transaction details of the counselling fee , you give the reference number of acknowledgment slip of the payment made to iit.
  img
Sher Mohammad 3 months ago
Can I give JEE 2015, if I already took admission in SVNIT ECE branch this year.My JEE marks is 197 and have passed CBSE Boards with 91.2 %.I wish to better performence next year and want to...
 
 
You are not allowed to apper in IIT JEE 2015 exam if you have already taken admission in any college. If you believe that you can get better rank next year then prepare for it. It is...
  img
Ramreddy 2 months ago
Hi I need help in deciding my third choice, my AIR is 114 and i can choose between IIT Bomaby Electrical or IIT Kanpur CS or IIT Madras CS, what is your suggestion please help.
 
 
Hi Arham, You should choose IIT B Electrical as your third choice. Research facility, placement & faculty of EE at Bombay are quite good. Good Luck! Thanks & Regards Jitender Singh...
  img
Jitender Singh 4 months ago
 
which branch do you like? you will be forced to struggle in cs if you actually like ee. electrical will give you a broader and safer base if you want to pursue higher studies but if cs is...
 
Vineet Vinayak 4 months ago
I attained a rank of 5500 in JEE Main.I would really like to pursue computer science. Which NIT can I expect to get?Also,should I go for Jadavpur University CSE or IIEST CSE instead of...
 
 
Hi, Visit our college and branch predictor for a better idea. Top NITs are better than the other oprions you provided....
  img
Yash Baheti 29 days ago
View all Questions »