Add :
`1/4 x^(2)y^(2) , 3x^(2)y^(2)`

Add : x^(2) y^(2) , 2x^(2)y^(2) , - 4x^(2)y^(2) , 6x^(2)y^(2)

Using horizontal method : Add x^(2)+y^(2)- 2xy , -2x^(2)-y^(2)-2xy and 3x^(2) +y^(2) +xy

Add : x^(3) - x^(2)y + 5xy^(2) + y^(3) , -x^(3) - 9xy^(2) + y^(3), 3x^(2)y + 9xy^(2)

Add : 5x^(2)-2xy +8y^(2), 3xy -7y^(2)-2x^(2) and y^(2)+xy-4x^(2) .

Factorise : x^(4) + y^(4) - 3x^(2)y^(2)

Add the following expressions: x^(2)-2xy+3y^(2), 5y^(2)+3xy-6x^(2)

The solution of the differential equation (dy)/(dx)+(x(x^(2)+3y^(2)))/(y(y^(2)+3x^(2)))=0 is (a) x^(4)+y^(4)+x^(2)y^(2)=c (b) x^(4)+y^(4)+3x^(2)y^(2)=c (c) x^(4)+y^(4)+6x^(2)y^(2)=c (d) x^(4)+y^(4)+9x^(2)y^(2)=c

Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+6y+1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=0

If the length of the tangent from (1,2) to the circle x^(2)+y^2+x+y-4=0 and 3x^(2)+3y^(2)-x+y+lambda=0 are in the ratio 4:3 then lambda=

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0