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Joint Entrance Examination
Mathematics
Parabola
Question 19
Question 19 of 198
Medium
MCQ
Let the focal chord PQ of the parabola
y
2
=
4
x
y^2=4 x
y
2
=
4
x
make an angle of
60
∘
60^{\circ}
6
0
∘
with the positive
x
x
x
axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the
y
y
y
-axis ...
A
15
B
25
C
20
D
30
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Solutions · 1
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Official solution
P
T
:
t
y
=
x
+
a
t
2
P
S
=
P
T
M
t
=
1
t
=
tan
30
∘
=
1
3
t
=
3
α
=
a
t
=
3
(
a
=
1
)
∴
5
α
2
=
15
\begin{gathered} PT:ty=x+a{t}^{2} \\ PS=PT \\ {M}_{t}=\frac{1}{t}=\tan {30}^{\circ }=\frac{1}{\sqrt{3}} \\ t=\sqrt{3} \\ \alpha =at=\sqrt{3}\, (a=1) \\ \therefore 5{\alpha }^{2}=15 \end{gathered}
P
T
:
t
y
=
x
+
a
t
2
P
S
=
P
T
M
t
=
t
1
=
tan
30
∘
=
3
1
t
=
3
α
=
a
t
=
3
(
a
=
1
)
∴
5
α
2
=
15
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