" (i) "f=x^(4)+x^(2)y^(2)+y^(4)

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

Factorize: 4x^2+12 x y+9y^2 (ii) x^4-10 x^2y^2+25 y^4 a^4-2a^2b^2+b^4

For the equations given below, tell the nature of graphs. (a) y =2x^(2) (b) y =-4x^(2) +6 (c) y = 6 ^(-4x) (d) y = 4(1 -e^(-2x)) (e) y =(4)/(x) (f) y =-(2)/(x)

For the equations given below, tell the nature of graphs. (a) y =2x^(2) (b) y =-4x^(2) +6 (c) y = 6 ^(-4x) (d) y = 4(1 -e^(-2x)) (e) y =(4)/(x) (f) y =-(2)/(x)

Find the least and greatest value of f(x,y) = x^(2) + y ^(2) - xy where x and y are connected by the relation x^(2)+4y^(2) = 4 .

Find the least and greatest value of f(x,y) = x^(2) + y ^(2) - xy where x and y are connected by the relation x^(2)+4y^(2) = 4 .

Find the least and the greatest value of f(x , y) = x^(2) + y^(2) - xy where x and y are connected by the relation x^(2) + 4y^(2) = 4

If x/y = (a + 2)/(a - 2) , then show that (x^(2) - y^(2))/(x^(2) + y^(2)) = (4a)/(a^(2) + 4) .