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

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

Prove that the curves x y=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.

The curves y=4x^(2)+2x-8 and y=x^(3)-x+13 touch each other at the point

The curves y=x^(2)+x+1 and 2y=x^(3)+5x touch each other at the point

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

The curves y=x^(3)+x+1 and 2y=x^(3)+5x touch each other at the point

Show that the curvesy ^(2)=4x and x^(2)+y^(2)-6x+1=0 touch each other at (1,2). Also find the equation of the common tangent and normal.

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