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JEE Advanced 2022 Paper 1
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© examsnet.com
Question : 13
Total: 54
Consider the parabola
y
2
=
4
x
. Let
S
be the focus of the parabola. A pair of tangents drawn to the parabola from the point
P
=
(
−
2
,
1
)
meet the parabola at
P
1
and
P
2
. Let
Q
1
and
Q
2
be points on the lines
S
P
1
and
S
P
2
respectively such that
P
Q
1
is perpendicular to
S
P
1
and
P
Q
2
is perpendicular to
SP
2
. Then, which of the following is/are TRUE ?
S
Q
1
=
2
Q
1
Q
2
=
3
√
10
5
PQ
1
=
3
SQ
2
=
1
Validate
Solution:
Let equation of tangent with slope '
m
' be
T
:
y
=
mx
+
1
m
T
: passes through
(
−
2
,
1
)
so
1
=
−
2
m
+
1
m
⇒
m
=
−
1
or
m
=
1
2
Points are given by
(
a
m
2
,
2
a
m
)
So, one point will be
(
1
,
−
2
)
&
(
4
,
4
)
Let
P
1
(
4
,
4
)
&
P
2
(
1
,
−
2
)
P
1
S
:
4
x
−
3
y
−
4
=
0
P
2
S
:
x
−
1
=
0
PQ
1
=
|
4
(
−
2
)
−
3
(
1
)
−
4
5
|
=
3
SP
=
√
10
;
PQ
2
=
3
;
SQ
1
=
1
=
SQ
2
1
2
(
Q
1
Q
2
2
)
×
√
10
=
1
2
×
3
×
1
(comparing Areas)
⇒
Q
1
Q
2
=
2
×
3
√
10
=
3
√
10
5
© examsnet.com
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