Equation of the circle of minimum radius which touches both the parabolas `y = x^2+2x+4` and `x-y^2+2y+4` is

The minimum area of circle which touches the parabolas y=x^(2)+1andy^(2)=x-1 is

Find the equation of the circle of minimum radius which contains the three cricles x^(2)-y^(2)-4y-5=0 x^(2)+y^(2)+12x+4y+31=0 and x^(2)+y^(2)+6x+12y+36=0

The equation of a line which touches both the parabola y^(2)=4x and the hyperbola 3x^(2)-4y^(2)=12 is

The equation to the line touching both the parabolas y^(2)=4x and x^(2)=-32y is

The equation of the circle, which touches the parabola y^2=4x at (1,2) and passes through the origin is :

Minimum area of the circle which touches the parabola y=x^(2)+1 and y^(2)=x-1 is (k pi)/(32) then k=

The radius of a circle, having minimum area, which touches the curve y=4-x^(2) and the lines y=|x|, is