Q65.If the circles (x + 1)2 + (y + 2)2 = r2 and x2 + y2 −4x −4y + 4 = 0 intersect at exactly two distinct points, then (1) 5 < r < 9 (2) 0 < r < 7 (3) 3 < r < 7 (4) 21 < r < 7
What This Question Tests
The question tests the condition for two circles to intersect at exactly two distinct points, which involves comparing the distance between their centers with the sum and difference of their radii.
Concepts Tested
Formulas Used
Distance formula d = √((x₂-x₁)² + (y₂-y₁)²)
|r₁ - r₂| < d < r₁ + r₂
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📋 Question Details
- Chapter
- Circles
- Topic
- Intersection of circles
- Year
- 2024
- Shift
- 30 Jan Shift 1
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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