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![[Post New]](/templates/default/images/icon_minipost_new.gif) 29 Mar 2008 12:22:47 IST
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IF A(cos@,sin@) , B(sin@,-cos@) and C(1,2) are vertices of the triangle ABC, then as @ varies, find the locus of its CENTROID
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29 Mar 2008 15:30:26 IST
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let centroid be (h,k)
h = (sin@ + cos@ + 1)/3
k= (sin@ - cos@ + 2)/3
=> 3h - 1 = sin@ + cos @
and
3k-2 = sin@ - cos@
square the 2 equations and add them
we get:
(3h-1)^2 + (3k-2)^2 = 2
so locus of centroid is:
(3x-1)^2 + (3y-2)^2 = 2
which is a circle of centre (1/3, 2/3) and radius (rt2)/3
:)
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29 Mar 2008 21:14:41 IST
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agree with hash_include
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