Prove that the curves `x y=4a n dx^2+y^2=8` touch each other.

Prove that the curves x y=4 and x^2+y^2=8 touch each other.

Prove that the curves xy=4 and x^(2)+y^(2)=8 touch each other.

Show that the curves x y=a^2 and x^2+y^2=2a^2 touch each other.

Prove that the curves y^2=4x and x^2+y^2-6x+1=0 touch each other at the points (1,\ 2) .

Let f(x) be a differentiable function and f(x)>0 for all x. Prove that the curves y=f(x) and y=sin kxf(x) touch each other at the points of intersection of the two curves.

Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other

Prove that the curves 2y^(2)=x^(3) and y^(2)=32x cut each other orthogonally at the origin

Prove that the curve y^(2)=4x and x^(2)+y^(2)-6x+1=0 touches each other at thepoint (1,2), find the equation of the common tangents.

Prove that the curve x^(2)+y^(2)=1 and y^(2)=4(x-1) touches each other.

Find the value of a,b,c such that curves y=x^(2)+ax+bandy=cx-x^(2) will touch each other at the point (1,0)