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ISI Entrance Examination
2012 ISI Entrance Examination
7
7
Part of
2012 ISI Entrance Examination
Problems
(1)
Locus of the centre of Gamma
Source: ISI 2012 #7
5/13/2012
Let
Γ
1
,
Γ
2
\Gamma_1,\Gamma_2
Γ
1
,
Γ
2
be two circles centred at the points
(
a
,
0
)
,
(
b
,
0
)
;
0
<
a
<
b
(a,0),(b,0);0<a<b
(
a
,
0
)
,
(
b
,
0
)
;
0
<
a
<
b
and having radii
a
,
b
a,b
a
,
b
respectively.Let
Γ
\Gamma
Γ
be the circle touching
Γ
1
\Gamma_1
Γ
1
externally and
Γ
2
\Gamma_2
Γ
2
internally. Find the locus of the centre of of
Γ
\Gamma
Γ
conics
ellipse
geometry proposed
geometry