for the variable triangle ABC with fixed vertex C(1,2) and A,B having coordinates (cost,sint) , (sint,-cost) respectively , find the locus of its centroid

Dear krishnan,

coordinates of orthocentre for this triangle (cost +sint +1)/3 , (sint - cost +2 )/3

h = (cost +sint +1)/3     k =   (sint - cost +2 )/3

(3h-1)²= (cost +sint)² ---1     (3k-2)² = (sint - cost)²---2             

now squaring 1 and 2 and adding them we get

9(h²+k²)-6h -12k +3 = 0 

now replacing h , k by x, y

9(x²+y²)-6x -12y +3 = 0   is the locus of the coordinates of centeroid 

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