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JEE Main 20206 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2020 · 6 September · Morning Shift · Mathematics · Complex Number

The region represented by z = x + iy ∈ C: | z | - Re ( z ) ≤ 1 is...

The region represented by z=x+iy∈C:∣z∣−Re(z)≤1{ z = x + iy \in C: | z | - Re ( z ) \le 1 } is also given by the inequality

Options

  1. Ay2≥2(x+1){y}^{2} \ge 2 ( x + 1 )
  2. By2≤2(x+12){y}^{2} \le 2\left(x + \dfrac{1}{2}\right)
  3. Cy2≤(x+12){y}^{2} \le \left(x + \dfrac{1}{2}\right)
  4. Dy2≥x+1{y}^{2} \ge x + 1

Correct answer

B. y2≤2(x+12){y}^{2} \le 2\left(x + \dfrac{1}{2}\right)

Step-by-step solution

x2+y2−x≤1\sqrt{{x}^{2} + {y}^{2}} - x \le 1
⇒x2+y2≤x+1⇒ \sqrt{{x}^{2} + {y}^{2}} \le x + 1
⇒x2+y2≤x2+2x+1⇒ {x}^{2} + {y}^{2} \le {x}^{2} + 2x + 1
⇒y2≤2x+1⇒ {y}^{2} \le 2x + 1
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