If `f(x , y)` satisfies the equation `1+4x-x^2=sqrt(9sec^2y+4cos e c^2y)` then find the value of `xa n dtan^2ydot`

Solve the equation tan^4x+tan^4y+2cot^2xcot^2y=3+sin^2(x+y) for the values of xa n dydot

If sin^(-1)(x^2-4x+5)+cos^(-1)(y^2-2y+2)=pi/2 then find the value of xa n dydot

If (x^2)/4+(y^2)/9=1, then find the range of 2x+ydot

If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)1/x+cos^(-1)1/ydot

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_____

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 y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

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 the locus of the moving poin P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a.