Question
Let the set of all values of r, for which the circles (x+1)^ 2 +(y+4)^ 2 =r^ 2 and x^ 2 +y^ 2 -4 x-2 y-4=0 intersect at two distinct points be the interval ( , ). Then is equal to
JEE Main
Mathematics
Circle
2026
JEE Main 2026 (22 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 21
- B. 24
- C. 20
- D. 25
Answer
D. 25
Step-by-step solution
Circle 1: center C_1 = (-1, -4), radius r. Circle 2: (x-2)^2 + (y-1)^2 = 9, center C_2 = (2, 1), radius 3. Distance d = 9+25 = 34 . For two intersection points: |r-3| r + 3 > 34 r > 34 -3 and |r-3| r ( 34 -3,\ 34 +3), so = 34 -3, = 34 +3. = ( 34 )^2 - 9 = 34 - 9 = 25.
Related: Mathematics — Circle · All PYQ Banks