More than enough info!
A rectangular hyperbola is cut by a circle of radius 2 units in 4 distinct points A , B , C and D .Let O be the center of the rectangular hyperbola.
Find the maximum value of O A + O B + O C + O D .
The answer is 8.00.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
2 solutions
Hint:Cauchy Schwartz might be helpful.
You know what I did.Simply take a circle with centre as origin and the rectangular hyperbola with the same centre.So the ans would be 2 + 2 + 2 + 2 = 8 .Although I guess its gonna be done in formal way as O A 2 + O B 2 + O C 2 + O D 2 = 4 R 2 .Then using Cauchys inequality yields the sum is O A + O B + O C + O D < = 8 .So the maximum is 8.
Log in to reply
Yup the last one is the thing I did.And yes your first statement is the equality condition.
Log in to reply
Good.keep posting more maths problems
Log in to reply
@Spandan Senapati – Yup if I come across any good one I will post.You aso post some jee lvl physics probs!
Log in to reply
@Harsh Shrivastava – Ya sure....I will post some good jee questions.....And I haven't posted a maths q till now!!
@Harsh Shrivastava – Hey can you just help me-I encountered (lni) today.Is its value ( ( 2 n + 1 / 2 ) π or simply π / 2 ).confused....
Log in to reply
@Spandan Senapati – What is ini?Intigration?
I'll try my best.Post it!
Log in to reply
@Harsh Shrivastava – No its rather logi(base e) or natural logarithm of i.is the square root of -1.(just to make clear)
Log in to reply
@Spandan Senapati – If you talk about principle value then it is just pi/2.Else since ln is a multivalued function,we have that general solution.
Bro your marks in inpho?selected?
Log in to reply
No I did nt get selected.Will try next yr.I guess 3 from 11 and 34 from 12th have been selected.I could not complete my paper and had messed up the graphs...which carried more than 25 marks.
Not even sarthak..We were the only 2 from 11th from odisha and only 7 appeared for inpho😀😀
Bro comment on the kvpy interview forum.This is meant for discussions to your problem I guess.cheers.☺☺
Yep i did the same!. I Will be posting jee level problems after mains most probably when i will revise for jee advanced
Log in to reply
OK.....BTW you got selected in chem??
Log in to reply
@Spandan Senapati – Well not actually . Paper had loads of extra jee stuff (biochemistry and biomolecules) which i didn't prepared due to lack of time and of course i did not wanted to deviate from jee syllabus
Log in to reply
@Prakhar Bindal – No issues.Jee is more imp.Even I didn't get selected in inpho.although I worked hard this time.But as of now since my jee physics is almost over I will work hard this time again for inpho.
Log in to reply
@Spandan Senapati – Well cool . i am sure you will get through next year. Best of luck!.
Even i had minimum expectations from myself hence i didn't found it shocking or so
Log in to reply
@Prakhar Bindal – Best of luck..go on you have a lot many xms awaiting for you......I am sure you will give your best.......Best of luck☺☺(fav smiley)
@Prakhar Bindal – Ya olympiads courses generally diverge from jee syllabi.
Yeah.....did the same way!!!!
the MOTHER of over-rated questions :P Simply take a circle with centre as origin and the rectangular hyperbola with the same centre.So the ans would be 8 .Although I guess its gonna be done in formal way as using Cauchys inequality yields the sum is 8 .So the maximum is 8.