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JEE Advanced Model Paper 8 with solutions for online practice
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© examsnet.com
Question : 41
Total: 84
Let P and Q be two points denoting the complex numbers α and β respectivelyon the complex plane. Which of the following equations can represent the equationof the circle passing through P and Q with least possible area ?
arg
(
z
−
α
z
−
β
)
=
π
2
Re (z - α)
–
–
–
–
–
–
(
z
−
β
)
= 0
|
z
−
α
|
2
+
|
z
−
β
|
2
=
–
–
–
–
–
–
|
α
−
β
|
2
z
−
z
+
(
−
α
+
−
β
2
)
z +
(
α
+
β
2
)
−
z
+ α
−
β
+
−
α
β = 0
Validate
Solution:
(a) option is not correct as it should be ±
π
2
(b) Equation of circle is
z
−
α
α
β
is purely imaginary
∴ Re
(
z
−
α
z
−
β
)
= 0 or ∴ Re (z - α) (
−
z
−
β
) = 0 ⇒ (b) is correct
(c) Option is obviously correct
(d) Option can not be correct at the centre of required circle is
(
α
+
β
2
)
but from the given equationcentre of the circle is coefficient
−
z
= -
(
α
+
β
2
)
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