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EAMCET Engineering 2006 Solved Paper
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© examsnet.com
Question : 101
Total: 160
The equation of the locus of
z
such that
|
z
−
i
z
+
i
|
=
2
where
z
=
x
+
i
y
is a complex number, is
3
x
2
+
3
y
2
+
10
y
−
3
=
0
3
x
2
+
3
y
2
+
10
y
+
3
=
0
3
x
2
−
3
y
2
−
10
y
−
3
=
0
x
2
+
y
2
−
5
y
+
3
=
0
Validate
Solution:
|
z
−
i
z
+
i
|
=
2
∵
|
x
+
i
y
−
i
x
+
i
y
+
i
|
=
2
∴
|
x
+
(
y
−
1
)
i
x
+
(
y
+
1
)
i
|
=
2
⇒
|
x
+
i
(
y
−
1
)
|
=
2
|
x
+
(
y
+
1
)
i
|
⇒
x
2
+
(
y
−
1
)
2
=
4
(
x
2
+
(
y
+
1
)
2
)
⇒
x
2
+
y
2
−
2
y
+
1
=
4
y
2
+
8
y
+
4
+
4
x
2
⇒
3
x
2
+
3
y
2
+
10
y
+
3
=
0
© examsnet.com
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