If `x , y in R` satisfies `(x+5)^2+(y-12)^2=(14)^2,` then the minimum value of `sqrt(x^2+y^2)` is__________

If x ,y in R and x^2+y^2+x y=1, then find the minimum value of x^3y+x y^3+4.

If x,y,in R^(+) satisfying x+y=3 , then the maximum value of x^2y is _____________.

If (x,y) lies on the ellipse x^(2)+2y^(3) = 2 , then maximum value of x^(2)+y^(2)+ sqrt(2)xy - 1 is

Suppose xa n dy are real numbers and that x^2+9y^2-4x+6y+4=0 . Then the maximum value of ((4x-9y))/2 is__________

For any x,y, in R,xygt0 . Then the minimum value of (2x)/(y^3)+(x^3y)/(3)+(4y^2)/(9x^4) is ___________.

Given that x,y,z are positive reals such that xyz=32 . The minimum value of x^2+4xy+4y^2+2z^2 is ___________.

If x ,y in R satify the equation x^2+y^2-4x-2y+5=0, then the value of the expression [(sqrt(x)-sqrt(y))^2+4sqrt(x y)]//(x+sqrt(x y)) is a. sqrt(2)+1 b. (sqrt(2)+1)/2 c. (sqrt(2)-1)/2 d. (sqrt(2)+1)/(sqrt(2))

If R={(x,y): x,y in W, x ^(2)+y^(2)=25} , then find the domain and range or R.

If x ,y in R , satisfies the equation ((x-4)^2)/4+(y^2)/9=1 , then the difference between the largest and the smallest valus of the expression (x^2)/4+(y^2)/9 is_____