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

Question

Let $A = \{ (x,y) \in R \times R|2{x^2} + 2{y^2} - 2x - 2y = 1\} $, $B = \{ (x,y) \in R \times R|4{x^2} + 4{y^2} - 16y + 7 = 0\} $ and $C = \{ (x,y) \in R \times R|{x^2} + {y^2} - 4x - 2y + 5 \le {r^2}\} $.

Then the minimum value of |r| such that $A \cup B \subseteq C$ is equal to

${{3 + \sqrt {10} } \over 2}$

${{2 + \sqrt {10} } \over 2}$

${{3 + 2\sqrt 5 } \over 2}$

$1 + \sqrt 5 $

Solution

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