jee-main 2024 Q65

jee-main · India · session1_30jan_shift1 Circles Intersection of Circles or Circle with Conic
If the circles $( x + 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = r ^ { 2 }$ and $x ^ { 2 } + y ^ { 2 } - 4 x - 4 y + 4 = 0$ intersect at exactly two distinct points, then
(1) $5 < \mathrm { r } < 9$
(2) $0 < \mathrm { r } < 7$
(3) $3 < r < 7$
(4) $\frac { 1 } { 2 } < \mathrm { r } < 7$
If the circles $( x + 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = r ^ { 2 }$ and $x ^ { 2 } + y ^ { 2 } - 4 x - 4 y + 4 = 0$ intersect at exactly two distinct points, then\\
(1) $5 < \mathrm { r } < 9$\\
(2) $0 < \mathrm { r } < 7$\\
(3) $3 < r < 7$\\
(4) $\frac { 1 } { 2 } < \mathrm { r } < 7$