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Byju's Answer
Standard XII
Mathematics
Proof of LaGrange's Mean Value theorem
If the tangen...
Question
If the tangent to the curve x = a t
2
, y = 2 at is perpendicular to x-axis, then its point of contact is
(a) (a, a)
(b) (0, a)
(c) (0, 0)
(d) (a, 0)
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Solution
(c) (0, 0)
Let the required point be (x
1
, y
1
).
Since
,
the
point
lies
on
the
curve
.
Hence
,
x
1
=
a
t
2
and
y
1
=
2
a
t
Now
,
x
=
a
t
2
and
y
=
2
a
t
⇒
d
x
d
t
=
2
a
t
and
d
y
d
t
=
2
a
⇒
d
y
d
x
=
d
y
d
t
d
x
d
t
=
2
a
2
a
t
=
1
t
=
2
a
y
Slope of the tangent =
d
y
d
x
x
1
,
y
1
=
2
a
y
1
It is given that the tangent is perpendicular to the
y
-axis.
It means that it is parallel to the
x
-axis.
∴ Slope of the tangent = Slope of the
x
-axis
2
a
y
1
=
0
⇒
a
=
0
Now
,
x
1
=
a
t
2
=
0
and
y
1
=
2
a
t
=
0
∴
x
1
,
y
1
=
0
,
0
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0
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Proof of LaGrange's Mean Value theorem
Standard XII Mathematics
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