JEE Main 2023MathematicsComplex NumberHardNumerical

JEE Main 2023 — Complex Number Question with Solution

JEE Main 2023 (06 Apr Shift 2)

Question

For α, β, z∈ℂ and λ>1, if λ-1 is the radius of the circle z-α2+z-β2=2λ, then α-β is equal to _____.

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Given,

α, β, z∈ℂ and λ>1,

And λ-1 is the radius of the circle z-α2+z-β2=2λ 

Now we know that equation of circle is given by,

z-z12+z-z22=z1-z22, where radius is given by r=z1-z22,

On comparing with z-α2+z-β2=2λ, we get

Radius z1-z22=α-β2 and α-β2=2λ

⇒α-β2=λ-1 given

⇒α-β=2λ-1 

⇒α-β2=4λ-1

⇒2λ=4λ-1

⇒λ=2

Hence, α-β2=4⇒α-β=2

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About this question

This is a previous-year question from JEE Main 2023, covering the Complex Number chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.