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EAMCET Engineering 2008 Solved Paper
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© examsnet.com
Question : 101
Total: 160
The points in the set
{
z
∈
C
:
arg
(
z
−
2
z
−
6
i
)
=
π
2
}
(where
C
denotes the set of all complex numbers) lie on the curve which is a
circle
pair of lines
parabola
hyperbola
Validate
Solution:
Given that,
arg
(
z
−
2
z
−
6
i
)
=
π
2
∴
arg
(
z
−
2
)
−
arg
(
z
−
6
i
)
=
π
2
Let
z
=
x
+
i
y
⇒
arg
[
(
x
−
2
)
+
i
y
]
−
arg
[
x
+
i
(
y
−
6
)
]
=
π
2
⇒
tan
−
1
y
x
−
2
−
tan
−
1
y
−
6
x
=
π
2
⇒
(
y
x
−
2
−
y
−
6
x
1
+
y
x
−
2
⋅
y
−
6
x
)
=
tan
π
2
⇒
x
(
x
−
2
)
+
y
(
y
−
6
)
=
0
This is an equation of circle in diametric form.
© examsnet.com
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