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Joint Entrance Examination
Mathematics
Parabola
Question 191
Question 191 of 198
Medium
MCQ
If \[\mathrm{P}(\mathrm{h}, \mathrm{k})\] be a point on the parabola
x
=
4
y
2
x=4 y^{2}
x
=
4
y
2
, which is nearest to the point \[\mathrm{Q}(0,33)\], then the distance of \[\mathrm{P}\] from the directrix of the parabola \[\quad y^{2}=4(x+y)\] is equal to :
A
8
B
2
C
6
D
4
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Official solution
Equation of normal \[y = - tx + 2.{1 \over {16}}t + {1 \over {16}}{t^3}\] \[33 = {t \over 8} + {{{t^3}} \over {16}}\] \[ \Rightarrow {t^3} + 2t = 528\]
t
=
8
t = 8
t
=
8
(
a
t
2
,
2
a
t
)
=
(
4
,
1
)
(a{t^2},2at) = (4,1)
(
a
t
2
,
2
a
t
)
=
(
4
,
1
)
Distance from
x
=
−
2
x = - 2
x
=
−
2
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