If `A(cosalpha,sinalpha),B(sinalpha,-cosalpha),C(1,2)` are the vertices of ` A B C ,` then as `alpha` varies, find the locus of its centroid.

Options

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

Answer

3

Explanation

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`