A rod of length 3l units, slides with its ends A and B on the x and y axes respectively. Then the locus of the centroid of △OAB is (Here, O is the origin.)
A
x2+y2=l2
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B
x2+y2=9l2
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C
3x2+3y2=l2
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D
x2+y2=3l2
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Solution
The correct option is Ax2+y2=l2 Let A(a,0),B(0,b) be the ends of the rod.
Let G(h,k) be the centroid of △OAB. ∴h=a+0+03=a3,k=0+b+03=b3 ⇒a=3h,b=3k
In △OAB, OA2+OB2=AB2 ⇒a2+b2=(3l)2 ⇒9h2+9k2=9l2 ⇒h2+k2=l2 ∴ Locus of G(h,k) is x2+y2=l2