`12xy(9x^2-16y^2) -: 4xy(3x + 4y) `.

Factorise 4x^2 + y^2 + z^2 - 4xy - 2yz + 4xz .

Work out the following divisions : 9x^2y^2 (3z – 24) -: 27xy(z – 8)

The latus rectum of a hyperbola 9x^(2) - 16y^(2) + 72x-32y-16 = 0 is :

The differential equation of all conics whose centre k lies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

If px^2-10xy + 12y^2+ 5x - 16y - 3 = 0 represents a pair of straight lines, then value of p is :

If x = 1, y = 3, z = 4, find the value of x^2 + 9y^2 + 4z^2 - 6xy + 12yz -4zx .

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is x-y+1 = 0 is x^2 + y^2 + 2xy - 4x + 4y - 4=0 .