Circle and ellipse together, god knows what to do

Calculus Level 4

Find the equation of ellipse \(\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1\) that has least area but contains the circle \((x-1)^{2} + y^{2} = 1\). If \(a^{2} + b^{2} = 2n\). Find the value of \(n\).

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