Find the shortest distance between two parabolas `y^(2)=x-2` and `x^(2)=y-2`

Find the shortest distance between the ellipse x^(2) + 2y^(2) = 2 and the circle x^(2)+y^(2)-3x-2sqrt(2)y +4=0

Find the area of the region bounded by the parabolas y^(2)=4x and x^(2)=4y

Find the area of the region bounded by the two parabolas y = x^(2) and y^(2) = x .

The shortest distance between two lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-4)/(4)=(z-5)/(5) is

Find the shortest distance between the lines (x-3)/(3)=(y-8)/(-1)=(z-3)/(1) and (x+3)/(-3)=(y+7)/(2)=(z-6)/(4)

Find the distance between the planes 2x-y+2z-7=0 and 6x-3y+6z+5=0 .

Find the distance between the planes 2x-y+2z-7=0 and 6x-3y+6z+5=0 .

The shortest distance between the line y-x =1 and the curve x=y^2 is