PROBLEMS
04

PARABOLA
Page
1
( 1 )
Find
the
coordinates
of
the
focus,
length
of
the
latusrectum
and
equation
of
the
directrix
of
the
parabola
x
2
=

8y.
[ Ans:
( 0,

2 ),
8,
y
=
2 ]
( 2 )
If
the
line
3x
+
4y
+
k
=
0
is
a
tangent
to
the
parabola
y
2
=
12x,
then
find
k
and
obtain
the
coordinates
of
the
point
of
contact.
=
8
,
3
16
16,
k
:
Ans

( 3 )
Derive
the
equations
of
the
tangents
drawn
from
the
point
( 1,
3 )
to
the
parabola
y
2
=
8x.
Obtain
the
coordinates
of
the
point
of
contact.
+
=
+
=
2
,
2
1
at
1
2x
y
and
)
4
2,
(
at
2
x
y
:
Ans
( 4 )
Find
the
equation
of
the
chord
of
the
parabola
joining
the
points
P ( t
1
)
and
Q ( t
2
).
If
this
chord
passes
through
the
focus,
then
prove
that
t
1
t
2
=

1.
[ Ans:
( t
1
+
t
2
)y
=
2 ( x
+
a t
1
t
2
) ]
( 5 )
If
one
endpoint
of
a
focal
chord
of
the
parabola
y
2
=
16x
is
( 9,
12 ),
then
find
its
other
endpoint.
3
16
,
9
16
:
Ans

( 6 )
The
points
P ( t
1
),
Q ( t
2
)
and
R ( t
3
)
are
on
the
parabola
y
2
=
4ax.
Show
that
the
area
of
triangle
PQR
is
a
2
l
( t
1

t
2
) ( t
2

t
3
) ( t
3

t
1
)
l
.
( 7 )
If
the
focus
of
the
parabola
y
2
=
4ax
divides
a
focal
chord
in
the
ratio
1
:
2,
then
find
the
equation
of
the
line
containing
this
focal
chord.
[ Ans:
y
=
±
2
2
( x

a ) ]
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PROBLEMS
04

PARABOLA
Page
2
( 8 )
If
a
focal
chord
of
the
parabola
y
2
=
4ax
forms
an
angle
of
measure
θ
with
the
positive
Xaxis,
then
show that
its
length
is
4
l
a
l
cosec
2
θ
.
( 9 )
Show
that
the
length
of
the
focal
chord
of
the
parabola
y
2
=
4ax
at
the
point
P ( t )
is
l
a
l
2
t
1
t
+
( 10 )
Find
the
condition
for
the
line
x cos
α
+
y sin
α
=
p
to
be
a
tangent
to
the
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 Spring '06
 Jones
 Tan

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