Let \(A=\left{(x,y)\in R\times R∣2{x}^{2}+2{y}^{2}-2x-2y=1\right}\\ B=\left{(x,y)\in R\times R∣4{x}^{2}+4{y}^{2}-16y+7=0…

Let

\(A=\left{(x,y)\in R\times R∣2{x}^{2}+2{y}^{2}-2x-2y=1\right}\\ B=\left{(x,y)\in R\times R∣4{x}^{2}+4{y}^{2}-16y+7=0\right}\text{ and }\\ C=\left{(x,y)\in R\times R∣{x}^{2}+{y}^{2}-4x-2y+5\leq {r}^{2}\right}\)
Then the minimum value of \(|r|\) such that \(A\cup B\subseteq C\) is equal to :

[JEE Main 2021, 27 Jul (Shift 1)]