JEE AdvancedCircleMedium
Question
If the two circles (x -1)2 + ( y - 3)2 = r2 and x2 + y2 -8x + 2y + 8 = 0 intersect in two distinct points. then
Options
A.2 < r < 8
B.r < 2
C.r = 2
D.r > 2
Solution
As, the two circles intersect in two distinct points.
⇒ distance between centres lies between |r1 - r2| and |r1 + r2|
ie,
⇒ |r - 3 | < 5 < | r + 3 |
⇒ r < 8 or r > 2
∴ 2 < r < 8
⇒ distance between centres lies between |r1 - r2| and |r1 + r2|
ie,
⇒ |r - 3 | < 5 < | r + 3 |
⇒ r < 8 or r > 2
∴ 2 < r < 8
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