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Question

lf t is parameter, A=(asect,btant) and B=(atant,bsect) , O=(0,0) then the locus of the centroid of ΔOAB is

A
9xy=ab
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B
xy=9ab
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C
x29y2=a2b2
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D
x2y2=19(a2b2)
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Solution

The correct option is A 9xy=ab
Let the centroid be G,
Then
G=(x1+x2+x33,y1+y2+y33)
Here
(x1,y1)=(asect,btant)
(x2,y2)=(atant,bsect)
(x3,y3)=(0,0)
Hence
G=(asectatant3,btant+bsect3)
Or
G(x,y)=(asectatant3,btant+bsect3)
Therefore
x=asectatant3
Or
3x=asectatant ..(i)
And
y=bsect+btant3
Or
3y=bsect+btant ...(ii)
Hence
3x×3y=(asectatant)(bsect+btant)
9xy=ab(secttant)(sect+tant)
9xy=ab(sec2ttan2t)
9xy=ab(1)
Or
9xy=ab

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