If the curves `x^(2/3)+y^(2/3)= c^(2/3) and x^2/a^2+y^2/b^2=1` touches each other, then which of the following is/are true?

If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) touch each other, then

If the circles (x-a)^(2)+(y-b)^(2)=c^(2) and (x-b)^(2)+(y-a)^(2)=c^(2) touch each other, then

Show that curves x^(2//3)+y^(2//3)=e^(2//3) and (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 may touch each other if c=a+b .

If c=a+b, then show that the curves x^((2)/(3))+y^((2)/(3))=c^((2)/(3)) and (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touch each other.

If the curve ax^(2) + 3y^(2) = 1 and 2x^2 + 6y^2 = 1 cut each other orthogonally then the value of 2a :

If circles (x -1)^(2) + y^(2) = a^(2) " and " (x + 2)^(2) + y^(2) = b^(2) touch each other externally , then

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

The curves 2x^(2) + 3y^(2) = 1 and cx^(2) + 4y^(2) = 1 cut each other orthogonally then the value of c is:

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