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Byju's Answer
Standard XII
Mathematics
Distance Formula Using Complex Numbers
| z -2/ z -3|...
Question
If
∣
∣
∣
z
−
2
z
−
3
∣
∣
∣
=
2
represents a circle whose radius is
r
, then the value of
3
r
is
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Solution
Let
z
=
x
+
i
y
∣
∣
∣
z
−
2
z
−
3
∣
∣
∣
=
2
⇒
|
z
−
2
|
2
=
4
|
z
−
3
|
2
⇒
(
x
−
2
)
2
+
y
2
=
4
[
(
x
−
3
)
2
+
y
2
]
⇒
3
x
2
+
3
y
2
−
24
x
+
4
x
+
36
−
4
=
0
⇒
x
2
+
y
2
−
20
3
x
+
32
3
=
0
Radius of the circle is
r
=
√
100
9
−
32
3
⇒
r
=
2
3
∴
3
r
=
2
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Distance Formula Using Complex Numbers
Standard XII Mathematics
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