Locus of centroid of the triangle whose vertices are

Asked by admin @ 13/08/2021 in Math viewed by 424 People

locus of centroid of the triangle whose vertices are (acost,asint),(bsint,-bcost)and(1,0),where t is the parameter , is

Answered by admin @ 13/08/2021

(acost,asint),(bsint,-bcost),(1,0)
Let locus of centroid be (h,k)
h=(acost+bsint+1)/3
3h-1=acost+bsint ------(1)
k=(asint-bcost+0)/3
3k=asint-bcost -------(2)
Squaring and adding (1) and (2) we get
(3h-1)²+(3k)²=a²+b²
Hence the locus is (3x-1)²+(3y)²=a²+b²

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