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Byju's Answer
Standard XII
Mathematics
Modulus of a Complex Number
Let z=1-t+i...
Question
Let
z
=
1
−
t
+
i
√
t
2
+
t
+
2
,
where
t
is a real parameter. The locus of
z
in the argand plane is:
A
a hyperbola
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B
an ellipse
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C
a straight line
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D
None of these
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Solution
The correct option is
A
a hyperbola
Let
z
=
x
+
i
y
, then
x
+
i
y
=
1
−
t
+
i
√
t
2
+
t
+
2
⇒
x
=
1
−
t
,
y
=
√
t
2
+
t
+
2
Putting
t
=
1
−
x
in the other relation, we get
y
2
=
t
2
+
t
+
2
=
(
1
−
x
)
2
+
1
−
x
+
2
=
(
x
−
3
2
)
2
+
7
4
⇒
y
2
−
(
x
−
3
4
)
2
=
7
4
,
which is a hyperbola.
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Similar questions
Q.
Let
z
=
1
−
t
+
i
√
t
2
+
t
+
2
, where
t
is a real parameter. The locus of
z
in Argand plane is
Q.
Let
z
=
1
−
t
+
i
√
t
2
+
t
+
2
, where
t
is real parameter. The locus of
z
in the Argand plane is
Q.
Let
z
=
1
−
t
+
i
√
t
2
+
t
+
2
, where
t
is a real parameter. The locus of
z
in Argand plane is
Q.
Let
z
=
(
1
−
t
)
+
i
√
t
2
+
t
+
2
where t is real parameter then locus of z in the Gaussian plane is
Q.
A
=
(
√
1
−
t
2
+
t
,
0
)
and
B
=
(
√
1
−
t
2
−
t
,
2
t
)
are two variable points where
t
is a parameter, the locus of the middle point of
A
B
is
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