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If `A(cosalpha,sinalpha),B(sinalpha,-cosalpha),C(1,2)`are thevertices of ` A B C ,`then as `alpha`varies,find the locus of its centroid.A. `x^(2)+y^(2)-2x-4y+1=0`B. `x^(2)+y^(2)-2x-4y+3=0`C. `3(x^(2)+y^(2))-2x-4y+1=0`D. None |
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Answer» Correct Answer - 3 SO let centroid is (h,k) `h=(cosalpha+sin alpha+1)/(3),K=(sin alpha-cosalpha +2)/(3)` ` implies cos alpha +sin alpha =3h -1 …..(i)` `implies sin alpha -cos alpha = 3K -2 …….(ii)` squaring and adding `2=(3h-1)^(2)+(3K-2)^(2)` locus` (3x-1)^(2)+(3y-2)^(2)=2` |
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