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Analytical Geometry

Blazing goIITian

Joined:	10 Oct 2011
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9 Jul 2012 18:12:31 IST

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a circle of constant radius r passes through the origin and meets the coordinate axes at p

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Analytical Geometry

a circle of constant radius r passes through the origin and meets the coordinate axes at point A and B respectively. Find the locus of the centroid of triangle OAB, O being the origin'

hint:(Ans=x^2+y^2=(4/9)r^2

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PALASH

Blazing goIITian

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9 Jul 2012 18:12:51 IST

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plz provide a detailed sol. i am very mu7ch confused in this..

Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5524

10 Jul 2012 08:05:41 IST

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As AOB is a right angle so AB will be diameter of circle. If A is (h,o) then B is (0, sqrt(4r^2-h^2)). Centroid of this triangle is (h/3,sqrt(4r^2-h^2)/3). Put x =3h in y = sqrt(4r^2-h^2)/3 and we get x^2 +y^2 = 4r^2/9

PALASH

Blazing goIITian

Joined: 10 Oct 2011

Posts: 430

10 Jul 2012 21:30:26 IST

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thnx

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