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Question

A straight line of length 9 units slides with its ends A,B always on x and y axes respectively. Locus of centroid of ΔOAB is

A
x2+y2=3
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B
x2+y2=9
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C
x2+y2=1
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D
x2+y2=8
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Solution

The correct option is A x2+y2=9
Let the centroid be (h,k) of two points always on x and y axes respectively.

let the points be A(a,o) and B(0,b) and O(0,0)

Now, to find h and k

h=0+0+a3 and k=0+0+b3

a=3h and b=3k

Distance Formula =(xx1)2+(yy1)2

Now using distance formula, we have

(3h)2+(3k)2=9

Squaring both sides

(3h)2+(3k)2=81

h2+k2=9

Therefore, locus of point is

x2+y2=9

471656_33766_ans_8d70ec92512e4aeda1e84f1614b500ef.jpg

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