y^(2)-xy(1-x)-x^(3)

The differential equation of all conics whose centre 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

The differential equation of all conics whose centre klies 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

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

The differential equation of all conics whose centre klies 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

The factors of x^(3)-x^(2)y-xy^(2)+y^(3) are (a (x+y)(x^(2)-xy+y^(2))(b)(x+y)(x^(2)+xy+y^(2))(c)(x+y)^(2)(x-y)(d)(x-y)^(2)(x+y)

Veriffy : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2))x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Equation of the tangent at (1,-1) to the curve x^(3)-xy^(2)-4x^(2)-xy+5x+3y+1=0 is

Equation of the tangent at (1,-1) to the curve x^(3)-xy^(2)-4x^(2)-xy+5x+3y+1=0 is

The factors of x^(3)-1+y^(3)+3xy are (a) (x-1+y)(x^(2)+1+y^(2)+x+y-xy)( b) (x+y+1)(x^(2)+y^(2)+1-xy-x-y)( c) (x-1+y)(x^(2)-1-y^(2)+x+y+xy)(d)3(x+y-1)(x^(2)+y^(2)-1)

If A=(x^3+y^3)/((x-y)^2+3xy), B=((x+y)^2-3xy)/(x^3-y^3), C=(xy)/(x^2-y^2) then (A-:B)xxC=