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JEE Mains 30-Jan-2023 Shift 1 Solved Paper
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© examsnet.com
Question : 75
Total: 90
If
P
(
h
,
k
)
be point on the parabola
x
=
4
y
2
, which is nearest to the point
Q
(
0
,
33
)
, then the distance of
P
from the directrix of the parabola
y
2
=
4
(
x
+
y
)
is equal to :
[30-Jan-2023 Shift 1]
2
4
8
6
Validate
Solution:
Equation of normal
y
=
−
t
x
+
2
a
t
+
a
t
3
y
=
−
t
x
+
2
16
t
+
1
16
t
3
It passes through
(
0
,
33
)
33
=
t
8
+
t
3
16
t
3
+
2
t
−
528
=
0
(
t
−
8
)
(
t
2
+
8
t
+
66
)
=
0
t
=
8
P
(
a
t
2
,
2
a
t
)
=
(
1
16
×
64
,
2
×
1
16
×
8
)
=
(
4
,
1
)
Parabola :
y
2
=
4
(
x
+
y
)
⇒
y
2
−
4
y
=
4
x
⇒
(
y
−
2
)
2
=
4
(
x
+
1
)
Equation of directix :-
x
+
1
=
−
1
x
=
−
2
Distance of point
=
6
Ans. : (4)
© examsnet.com
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