Q64.A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y −5 = 0 at two points P and Q such that PQ is a diameter of C1 . Then the diameter of C is : (1) 4√15 (2) √285 (3) 15 (4) 7√5 = 1 having eccentricity √52 . If the tangent and
What This Question Tests
This question requires constructing the equation of a circle given tangency conditions and then using the concept of the radical axis as a diameter for the intersection of two circles, leading to complex algebraic manipulation.
Concepts Tested
Formulas Used
(x-x₀)² + (y-y₀)² = r²
Equation of circle tangent to y-y₁=m(x-x₁) at (x₁, y₁): (x-x₁)²+(y-y₁)²+λ(y-y₁-m(x-x₁))=0
Radical axis S₁-S₂=0
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📋 Question Details
- Chapter
- Circles
- Topic
- Equation of a circle, intersection of circles
- Year
- 2021
- Shift
- 26 Aug Shift 2
- Q Number
- Q64
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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