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`

Prove that the locus of the centroid of the triangle whose vertices are (acost ,asint),(bsint ,-bcost), and (1,0) , where t is a parameter, is circle.

Find the coordinates of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3) .

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 locus of centroid of triangle formed by a tangent to the parabola y^(2) = 36x with coordinate axes is (a) y^(2) =- 9x (b) y^(2) +3x = 0 (c) y^(2) = 3x (d) y^(2) = 9x

(x+y)^3−(x−y)^3 can be factorized as (a) 2y(3x^2+y^2) (b) 2x(3x^2+y^2) (c) 2y(3y^2+x^2) (d) 2x(x^2 +3y^2)

Let R(x_1, y_1)a n dS(x_2,y_2) be the end points of latus rectum of parabola y^2=4xdot The equation of ellipse with latus rectum R S and eccentricity 1/2 are (a > b) ((3x+1)^2)/(64)+(3y^2)/8=1 ((3x-7)^2)/(64)+(3y^2)/8=1 ((3x+1)^2)/8+(3y^2)/(64)=1 ((3x-7)^2)/8+(3y^2)/(64)=1

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

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)a n d\ (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)

Multiply: (i) (2x^2-1)b y\ (4x^3+5x^2) (ii) (2x y+3y^2)(3y^2-2)

Factorize: 4\ (x+y)^2-28 y(x+y)+49 y^2 (2a+3b)^2+2(2a+3b)(2a-3b)+(2a-3b)^2