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JEE Mains 13-Apr-2023 Shift 1 Solved Paper
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© examsnet.com
Question : 24
Total: 90
Let
ω
=
z
z
+
k
1
z
+
k
2
i
z
+
λ
(
1
+
i
)
,
k
1
,
k
2
∈
R
. Let
Re
(
ω
)
=
0
be the circle
C
of radius 1 in the first quadrant touching the line
y
=
1
and the
y
-axis. If the curve
Im
(
ω
)
=
0
intersects
C
at
A
and
B
, then
30
(
AB
)
2
is equal to _______.
[13-Apr-2023 shift 1]
Your Answer:
Validate
Solution:
ω
=
z
z
+
k
1
z
+
k
2
i
z
+
λ
(
1
+
i
)
Re
(
ω
)
=
x
2
+
y
2
+
k
1
x
−
k
2
y
+
λ
=
0
Centre
≡
(
−
k
1
2
,
k
2
2
)
≡
(
1
,
2
)
⇒
k
1
=
−
2
,
k
2
=
4
radius
=
1
⇒
λ
=
4
Im
=
k
1
y
+
k
2
x
+
λ
=
0
∴
2
x
−
y
+
2
=
0
d
=
2
√
5
1
2
4
=
1
−
4
5
=
1
5
∴
301
2
=
24
© examsnet.com
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