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Analytical Geometry

Blazing goIITian

 Joined: 10 Oct 2011 Post: 430
9 Jul 2012 18:12:31 IST
1 People liked this
3
177
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

Blazing goIITian

Joined: 10 Oct 2011
Posts: 430
9 Jul 2012 18:12:51 IST
0 people liked this

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

Forum Expert
Joined: 29 Dec 2006
Posts: 5524
10 Jul 2012 08:05:41 IST
1 people liked this

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

Blazing goIITian

Joined: 10 Oct 2011
Posts: 430
10 Jul 2012 21:30:26 IST
0 people liked this

thnx

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