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.

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

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

Show that the circles x^(2)+y^(2)+2ax+c=0 and x^(2)+y^(2)+2by+c=0 touch each other if 1/(a^(2))+1/(b^(2))=1/c

If x : a = y : b = z : c , then prove that x^(3)/a^(2) + y^(3)/b^(2) + z^(3)/c^(2) = ((x+y+z)^(3))/((a+b+c)^(2))