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11

TWO
DIMENSIONAL
GEOMETRY
Page
1
( Answers
at
the
end
of
all
questions )
( 1 )
Area
of
the
greatest
rectangle
that
can
be
inscribed
in
an
ellipse
2
2
2
2
b
y
a
x
+
=
1
is
( a )
2ba
( b )
ab
( c )
ab
( d )
b
a
[ AIEEE
2005 ]
( 2 )
Let
P
be
the
point
( 1, 0 )
and
Q
the
point
on
the
locus
y
2
=
8x.
The
locus
of
midpoint
of
PQ
is
( a )
y
2

4x
+
2
=
0
( b )
y
2
+
4x
+
2
=
0
( c )
x
2
+
4y
+
2
=
0
( d )
x
2

4y
+
2
=
0
[ AIEEE
2005 ]
( 3 )
The
line
parallel
to
the
Xaxis
and
passing
through
the
intersection
of
the
lines
ax
+
2by
+
3b
=
0
and
bx

2ay

3a
=
0,
where
( a, b )
≠
( 0, 0 )
is
( a )
below
the
Xaxis
at
a
distance
2
3
from
it
( b )
below
the
Xaxis
at
a
distance
3
2
from
it
( c )
above
the
Xaxis
at
a
distance
2
3
from
it
( d )
above
the
Xaxis
at
a
distance
3
2
from
it
[ AIEEE
2005 ]
( 4 )
The
locus
of
a
point
P (
α
,
β
)
moving
under
the
condition
that
the
line
y
=
α
x
+
β
is
a
tangent
to
the
hyperbola
2
2
2
2
b
y
a
x

=
1
is
( a )
an
ellipse
( b )
a
circle
( c )
a
parabola
( d )
a
hyperbola
[ AIEEE
2005 ]
( 5 )
If
nonzero
numbers
a,
b,
c
are
in
H.P.,
then
the
straight
line
a
x
+
b
y
+
c
1
=
0
always
passes through
a
fixed
point.
That
point
is
( a )
(  1,
2 )
( b )
(  1,
 2 )
( c )
( 1,
 2 )
( d )
( 1,

2
1
)
[ AIEEE
2005 ]
( 6 )
If
a
vertex
of
a
triangle
is
( 1,
1 )
and
the
midpoint
of
two
sides
through
this
vertex
are
(  1,
2 )
and
( 3,
 2 ),
then
the
centroid
of
the
triangle
is
( a )
(  1,
3
7
)
( b )
( 
3
1
,
3
7
)
( c )
( 1,
3
7
)
( d )
(
3
1
,
3
7
)
[ AIEEE
2005 ]
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View Full Document 11

TWO
DIMENSIONAL
GEOMETRY
Page
2
( Answers
at
the
end
of
all
questions )
( 7 )
If
the
circles
x
2
+
y
2
+
2ax
+
cy
+
a
=
0
and
x
2
+
y
2

3ax
+
dy

1
=
0
intersect
in
two
distinct
points
P
and
Q,
then
the
line
5x
+
by

a
=
0
passes
through
P
and
Q
for
( a )
exactly
one
value
of
a
( b )
no
value
of
a
( c )
infinitely
many
values
of
a
( d )
exactly
two
values
of
a
[ AIEEE
2005 ]
( 8 )
A
circle
touches
the
Xaxis
and
also
touches
the
circle
with
centre
at
( 0,
3 )
and
radius
2.
The
locus of
the
centre
of
the
circle
is
( a )
an
ellipse
( b )
a
circle
( c )
a
hyperbola
( d )
a
parabola
[ AIEEE
2005 ]
( 9 )
If
a
circle
passes
through
the
point
( a,
b )
and
cuts
the
circle
x
2
+
y
2
=
p
2
orthogonally,
then
the
equation
of
the
locus
of
its
centre
is
( a )
x
2
+
y
2

3ax

4by
+
( a
2
+
b
2

p
2
)
=
0
( b )
2ax
+
2by

( a
2

b
2
+
p
2
)
=
0
( c )
x
2
+
y
2

2ax

3by ( a
2

b
2

p
2
)
=
0
( d )
2ax
+
2by

( a
2
+
b
2
+
p
2
)
=
0
[ AIEEE
2005 ]
( 10 )
An
ellipse
has
OB
as
semi
minor
axis,
F
and
F’
its
foci
and
the
angle
FBF’
is
a
right
angle.
Then
the
eccentricity
of
the
ellipse
is
( a )
2
1
( b )
2
1
( c )
4
1
( d )
3
1
[ AIEEE
2005 ]
( 11 )
If
the
pair
of
lines
ax
2
+
2 ( a
+
b ) xy
+
by
2
=
0
lie
along
diameters
of
a
circle
and
divide
the
circle
into
four
sectors
such
that
the
area
of
one
of
the
sectors
is
thrice
the
area
of
another
sector,
then
( a )
3a
2

10ab
+
3b
2
=
0
( b )
3a
2

2ab
+
3b
2
=
0
( c )
3a
2
+
10ab
+
3b
2
=
0
( d )
3a
2
+
2ab
+
3b
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This note was uploaded on 11/28/2011 for the course MATH 300 taught by Professor Jones during the Spring '06 term at ITT Tech Flint.
 Spring '06
 Jones
 Geometry

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