JEE AdvancedHardQuestion 320011
Question
The number of common tangents to circles x²+y²=4 and x²+y²−6x−8y+16=0 is:
- A3Correct
- B4
- C2
- D1
Correct answer
3
Explanation
Circle 1: centre O₁=(0,0), r₁=2. Circle 2: x²+y²−6x−8y+16=0 → centre O₂=(3,4), r₂=√(9+16−16)=3. Distance d = √(9+16)=5 = r₁+r₂ = 5. Since d = r₁+r₂, the circles are externally tangent → 3 common tangents (2 external + 1 common internal at point of tangency).