Show that the curves `x y=a^2a n dx^2+y^2=2a^2` touch each other

Explanation

curves are `xy= a^2`

`x^2 + y^2 = 2a^2`

`x^2 + (a^2/x)^2 = 2a^2`

`x^2 + a^4/x^2 = 2a^2`

`x^4 + a^4 = 2a^2x^2`

`x^4 + a^4 = 2a^2x^2`

`x^4 + a^4 - 2a^2x^2 = 0`

`(x^2 - a^2)^2 = 0`

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