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Mathematics
Mathematics
Problem
If
A
(
z
)
A(z)
A
(
z
)
is a variable point and
B
(
z
1
)
B(z_1)
B
(
z
1
)
,
C
(
z
2
)
C(z_2)
C
(
z
2
)
are fixed point such that
arg
(
z
−
z
1
z
2
−
z
1
)
=
θ
1
\arg\left(\frac{z-z_1}{z_2-z_1}\right) = \theta_1
ar
g
(
z
2
−
z
1
z
−
z
1
)
=
θ
1
and
arg
(
z
1
−
z
2
z
−
z
2
)
=
θ
2
\arg\left(\frac{z_1-z_2}{z-z_2}\right) = \theta_2
ar
g
(
z
−
z
2
z
1
−
z
2
)
=
θ
2
. If
tan
θ
1
/
2
tan
θ
2
/
2
=
3
2
\frac{\tan \theta_1/2}{\tan \theta_2/2} = \frac{3}{2}
t
a
n
θ
2
/2
t
a
n
θ
1
/2
=
2
3
, then locus of
A
A
A
is branch of hyperbola of eccentricity equal to - - -
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