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Joint Entrance Examination
Mathematics
Quadratic Equations and Inequalities
Question 76
Question 76 of 157
Medium
MCQ
The region represented by
{
z
=
x
+
i
y
∈
C
:
∣
z
∣
−
R
e
(
z
)
≤
1
}
\{z=x+iy\in\mathbb C: |z|-\mathrm{Re}(z)\le1\}
{
z
=
x
+
i
y
∈
C
:
∣
z
∣
−
Re
(
z
)
≤
1
}
is also given by the inequality:
A
y
2
≥
2
(
x
+
1
)
y^2 \ge 2(x+1)
y
2
≥
2
(
x
+
1
)
B
y
2
≤
2
(
x
+
1
2
)
y^2 \le 2\left(x+\dfrac12\right)
y
2
≤
2
(
x
+
2
1
)
C
y
2
≤
x
+
1
2
y^2 \le x+\dfrac12
y
2
≤
x
+
2
1
D
y
2
≥
x
+
1
y^2 \ge x+1
y
2
≥
x
+
1
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Official solution
\[\sqrt{x^2+y^2} \le 1+x \implies x^2+y^2 \le (1+x)^2 = 1+2x+x^2 \implies y^2 \le 1+2x = 2\left(x+\frac12\right)\]
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