Q62.For α, β, z ∈C and λ > 1 , if √λ −1 is the radius of the circle |z −α|2 + |z −β|2 = 2λ, then |α −β| is equal to _____.
What This Question Tests
The question requires transforming the given complex equation into a standard form of a circle and then relating its radius to the given radius to find the distance between two complex numbers.
Concepts Tested
Formulas Used
|z-z₀|² = R² (equation of circle)
|z-α|² + |z-β|² = 2λ => Equation of circle centered at (α+β)/2
📚 NCERT Sections This Tests
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2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Geometric interpretation of Complex Numbers
- Year
- 2023
- Shift
- 06 Apr Shift 2
- Q Number
- Q62
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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