Let A = (x,y) R × R|2x² + 2y² - 2x - 2y = 1, B = (x,y) R × R|4x² + 4y² - 16y + 7 = 0 and C = (x,y) R × R|x² + y² - 4x - 2y + 5 ≤ r². Then the minimum value of |r| such that A B C is equal to

Coordinate Geometry: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Morning shift · Q3024

JEE Main 202127 Jul, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

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

JEE Main 2021 · 27 Jul, Morning shift · Q3024

JEE Main 202127 Jul, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

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