Let A={(x,y)∈R×R | 2x²+2y²−2x−2y=1}... | Circles

JEE MAIN 2021

27-07-21 S1

Question

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

Select the correct option:

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

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

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

$1+\sqrt{5}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution