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VITEEE 2021 Paper
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Section:
Mathematics
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© examsnet.com
Question : 54
Total: 80
If the tangent at
P
(
1
,
1
)
on
y
2
=
x
(
2
−
x
)
2
meets the curve again at
Q
, then
Q
is
(
2
,
2
)
(
−
1
,
−
2
)
(
9
4
,
3
8
)
None of these
Validate
Solution:
y
2
=
x
(
2
−
x
)
2
⇒
y
2
=
x
3
−
4
x
2
+
4
x
.
.
.
(i)
⇒
2
y
dy
dx
=
3
x
2
−
8
x
+
4
⇒
dy
dx
=
3
x
2
−
8
x
+
4
2
y
[
dy
dx
]
P
=
3
−
8
+
4
2
=
−
1
2
∴ Equation of tangent at
P
is:
y
−
1
=
−
1
2
(
x
−
1
)
⇒
x
+
2
y
−
3
=
0
Using
y
=
3
−
x
2
in (i),
we get:
(
3
−
x
2
)
2
=
x
3
−
4
x
2
+
4
x
⇒
4
x
3
−
17
x
2
+
22
x
−
9
=
0
... (ii)
which has two roots 1,1(Because of (ii) being tangent at
(
1
,
1
)
)
.
Sum of 3 roots
=
17
4
∴
3
‌
rd
root
=
17
4
−
2
=
9
4
Then,
y
=
3
−
9
4
2
=
3
8
∴
Q
is
(
9
4
,
3
8
)
© examsnet.com
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