Let `M={(x, y)|y>=x^2}and N ={(x, y)|x^2+(y-a)^2<=1}` The necessary and sufficient condition for ` Mnn N=N`

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

Let S={(x,y)|x,y in R, x^2+y^2-10x+16=0} . The largest value of y/x can be put in the form of m/n where m, n are relatively prime natural numbers, then m^2+n^2=

Let the set C = {(x, y) | x^2- 2^y = 2023 , x, y in } . Then sum_((x,y) in C) (x y) is equal to _______.

Let's simplify:- (x + y) (x^2 -xy + y^2) + ( x - y) (x^2 + xy + y^2)

Let (x,y) = 2x y ^(2) + 3x ^(2) y calculate u _(x) (2,1) and u_(y) (1,-2).

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

Let x+(1)/(x)=2, y+(1)/(y)=-2 and sin^(-1)x+cos^(-1)y=m pi , then the value of m is