Locus of centroid of the triangle whose vertices are `(acost ,asint),(bsint-bcost)a n d(1,0),` where `t` is a parameter is: `(3x-1)^2+(3y)^2=a^2-b^2` `(3x-1)^2+(3y)^2=a^2+b^2` `(3x+1)^2+(3y)^2=a^2+b^2` `(3x+1)^2+(3y)^2=a^2-b^2`

Locus of centroid of the triangle whose vertices are (a cos t ,a s in t ), (b s in t ,-b cos t ) and (1, 0), where t is a parameter, is (3x-1)^2+(3y)^2=a^2-b^2 (3x-1)^2+(3y)^2=a^2+b^2 (3x+1)^2+(3y)^2=a^2+b^2 (3x+1)^2+(3y)^2=a^2-b^2

Locus of centroid of the triangle whose vertices are (acost, asint), (bsint,-bcost) and (1,0) where t is a parameter is : (A) (3x+1)^2 + (3y)^2 = a^2 - b^2 (B) (3x-1)^2 + (3y)^2 = a^2 - b^2 (C) (3x-1)^2 + (3y)^2 = a^2 + b^2 (D) (3x+1)^2 + (3y)^2 = a^2 + b^2

The centroid of the triangle with vertices at A(x_(1),y_(1)),B(x_(2),y_(2)),c(x_(3),y_(3)) is

If (-2,1) is the centroid of the triangle having its vertices at (x,0),(5,-2),(-8,y), then x,y satisfy the relation 3x+8y=0 (b) 3x-8y=0( c) 8x+3y=0 (d) 8x=3y

The centroid of the triangle formed by A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) is

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a)x+3y=2 (b) x+2y=2( c) x+y=2 (d) none of these

Factorize : (x+y)(2x+3y)-(x+y)(x+1)(x+y)(2a+b)-(3x-2y)(2a+b)

if |[2a,x_1,y_1],[2b,x_2,y_2],[2c,x_3,y_3]|=(abc)/2!=0 then the area of the triangle whose vertices are (x_1/a,y_1/a),(x_2/b,y_2/b),(x_3/c,y_3/c) is (A) (1/4)abc (B) (1/8)abc (C) 1/4 (D) 1/8

Show that the coordinates off the centroid of the triangle with vertices A(x_(1),y_(1),z_(1)),B(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3)) are ((x_(1)+x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3),(z_(1)+z_(2)+z_(3))/(3))

STATEMENT-1 : The centroid of a tetrahedron with vertices (0, 0,0), (4, 0, 0), (0, -8, 0), (0, 0, 12)is (1, -2, 3). and STATEMENT-2 : The centroid of a triangle with vertices (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_(3), z_(3)) is ((x_(1)+x_(2)+x_(3))/3, (y_(1)+y_(2)+y_(3))/3, (z_(1)+z_(2)+z_(3))/3)