The region represented by { z = x + i y ∈ C : | z | - Re ( z ) ≤ 1 } is also given by the…

The region represented by {z=x+iy∈C:|z|-Re(z)≤1} is also given by the inequality
  1. y2≥2(x+1)
  2. y2≤2x+12
  3. y2≤x+12
  4. y2≥x+1

Solution

 x2+y2-x≤1
⇒  x2+y2≤x+1
⇒  x2+y2≤x2+2x+1
⇒  y2≤2x+1
 

Asked in: JEE Main 2020 (06 Sep Shift 1)

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