((a)^(2))/(pi x^(2)+4y^(2))=4xyvec a,vec " th "x:y=?

Let y'=(4y^(2)+4xy+x^(2))/(4x^(2)) and y(1)=0 then y(e^((pi)/(2))) equals

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

The area bounded by the curves x^(2)+y^(2)=1,x^(2)+y^(2)=4 and the pair of lines sqrt(3)x^(2)+sqrt(3)y^(2)=4xy ,in the first quadrant is (1)(pi)/(2)(2)(pi)/(6)(3)(pi)/(4)(4)(pi)/(3)

If sin^(-1)x + sin^(-1)y = pi/2 prove that 2(x^(2) -x^(2)y^(2) + y^(2)) = 1 + x^(4) +y^(4) .

Statement 1: The equations of the straight lines joining the origin to the points of intersection of x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-2x-4y-4=0 is x-y=0 . Statement 2: y+x=0 is the common chord of x^(2)+y^(2)-4x-2y=4 and x^(2)+y^(2)-2x-4y-4=0

The angle between the circles x^(2)+y^(2)-4x-6y-3=0 . x^(2)+y^(2)+8x-4y+11=0 ( 1 - (pi)/(2) 2 - (pi)/(4) 3- (pi)/(3) 4- ( pi)/(6) )

If y=cos^(-1)((1)/(2sin x)) then (d^(2)y)/(dx^(2)) at ((pi)/(4),(pi)/(4)) is