JEE Main 2023MathematicsComplex NumberMediumMCQ

JEE Main 2023 — Complex Number Question with Solution

JEE Main 2023 (01 Feb Shift 1)

Question

If the center and radius of the circle z-2z-3=2 are respectively α,β and γ, then 3α+β+γ is equal to

Choose an option

Show full solutionCorrect option: D
Correct answer
D12

Step-by-step explanation

Given:

z-2z-3=2

Let z=x+iy, then we have

x-2+iyx-3+iy=2

⇒x-22+y2=2x-32+y2

⇒x2+y2-4x+4=4x2+4y2-24x+36

⇒3x2+3y2-20x+32=0

⇒x2+y2-203x+323=0

So, α,β≡103,0

And,

γ=1009-323=49=23

Therefore,

3α+β+γ=3103+23=12

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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.