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AIEEE 2009 Solved Paper
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© examsnet.com
Question : 77
Total: 89
The area of the region bounded by the parabola
(
y
−
2
)
2
=
x
−
1
, the tangent of the parabola at the point
(
2
,
3
)
and the
x
-axis is :
6
9
12
3
Validate
Solution:
The given parabola is
(
y
−
2
)
2
=
x
−
1
Vertex
(
1
,
2
)
and it meets
x
-axis at
(
5
,
0
)
Also it gives
y
2
−
4
y
−
x
+
5
=
0
So, that equation of tangent to the parabola at
(
2
,
3
)
is
y
.3
−
2
(
y
+
3
)
−
1
2
(
x
+
2
)
+
5
=
0
or
x
−
2
y
+
4
=
0
which meets
x
-axis at
(
−
4
,
0
)
.
In the figure shaded area is the required area.
Let us draw
P
D
perpendicular to
y
-axis.
Then required area
=
A
r
∆
B
O
A
+
A
r
(
O
C
P
D
)
−
A
r
(
△
A
P
D
)
=
1
2
×
4
×
2
+
3
∫
0
x
d
y
−
1
2
×
2
×
1
=
3
+
3
∫
0
(
y
−
2
)
2
+
1
d
y
=
3
+
[
(
y
−
2
)
3
3
+
y
]
0
3
=
3
+
[
1
3
+
3
+
8
3
]
=
3
+
6
=
9
Sq. units
© examsnet.com
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