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Analytical Geometry

Cool goIITian

Joined:	14 Mar 2008
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28 Mar 2008 13:26:59 IST

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626

circles:sqb..solution reqd...

None

tangents at the points (a cos(theta), a sin(theta) ), and (a cos(theta + pie /3), a sin(theta + pie/3) ) on a circle x^2+y^2= a^2 are drawn.then what is the locus of intersection of these tangents?

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akshay A NEW BEGINNING...

Blazing goIITian

Joined: 25 Dec 2007

Posts: 1104

28 Mar 2008 20:41:01 IST

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the locus is the MOJOR ARC OF A CIRCLE
that is we can say that it is a circle..

if my ans . is right plss tell i can give u solution..

RyuAmakusa

Blazing goIITian

Joined: 21 Mar 2008

Posts: 776

28 Mar 2008 21:32:55 IST

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i guess that will also be a circle

ankit aggarwal

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28 Mar 2008 22:52:23 IST

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the locus is 3x^2+3y^2=4a^2

sharmadon

Cool goIITian

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29 Mar 2008 19:37:11 IST

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yes its a circle..now pls post ur solutions...

ankit aggarwal

Blazing goIITian

Joined: 10 Feb 2008

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29 Mar 2008 21:30:30 IST

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cospie/6=a/IO
root3/2=a/x
x=2a/root3

now h^2+k^2=x^2
h^2+k^2=4a^2/3
3h^2+3k^2=4a^2
3x^2+3y^2=4a^2 ans.
see my next post for its diagram

akshay A NEW BEGINNING...

Blazing goIITian

Joined: 25 Dec 2007

Posts: 1104

29 Mar 2008 21:34:12 IST

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underoot of root3/2=a/x
x=2a/under root of 3

h²+ k²= x²
h² + k²= 4a² / 3

3h² + 3k²= 4a² -- ans..

RyuAmakusa

Blazing goIITian

Joined: 21 Mar 2008

Posts: 776

30 Mar 2008 01:58:53 IST

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yeah the ans is correct. i made a calc. mistake

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