IF A CIRCLE OF CONSTANT RADIUS 3K PASSES THROUGH THE ORIGIN MEETS THE COORDINATE AXES AT A AND B , THEN LOCUS OF THE CENTROID OF TRIANGLE OAB IS

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Please find below the solution to the asked query:

As OAOB, where O0,0 is origin, henceAOB=90° AB is diameter Angle in semi circle is 90°HenceAB=2r=6kLet coordinates of A be a,0 and that of Bbe 0,bBy distance formulaAB=a-02+0-b2=6ka2+b2=36k2...iLet coordinates of centroid be p,qp,q=0+a+03,0+0+b3a=3pb=3qSquare and adda2+b2=9p2+q2Use i9p2+q2=36k2p2+q2=4k2Hence locus isx2+y2=4k2 Answer  

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