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UPSC NDA I and II 2020 Math Solved Paper
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© examsnet.com
Question : 10
Total: 120
In the parabola,
y
2
=
x
,
what is the length of the chord passing through the vertex and inclined to the
x
-axis at an angle
θ
?
[NDA-I 2020]
sin
θ
.
sec
2
θ
cos
θ
.
cosec
2
θ
cot
θ
.
sec
2
θ
2
tan
θ
.
cosec
2
θ
Validate
Solution:
👈: Video Solution
Given parabola :
y
2
=
x
.
From standard equation of parabola
y
2
=
4
a
x
Focus
=
(
a
,
0
)
Here
a
=
1
4
∴ Focus of parabola
y
2
=
x
=
(
1
4
,
0
)
Vertex of the parabola
=
(
0
,
0
)
Let
P
(
t
2
4
,
t
2
)
lies on the parabola then, its slope
=
tan
(
θ
)
∴
t
2
t
2
4
=
tan
θ
⇒
t
=
2
cot
θ
So, point
P
(
t
2
4
,
t
2
)
=
(
cot
2
θ
,
cot
θ
)
Its distance from vertex
(
0
,
0
)
=
√
(
cot
2
θ
−
0
)
2
+
(
cot
θ
−
0
)
2
=
cot
θ
√
cot
2
θ
+
1
=
cot
θ
.
cosec
θ
=
cos
θ
.
cosec
2
θ
© examsnet.com
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