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Standard XII
Mathematics
Question
If the curve
(
x
a
)
n
+
(
y
b
)
n
=
2
touches the straight line
x
a
+
y
b
=
2
, then find the value of
n
.
2
3
4
any real number
A
2
B
any real number
C
3
D
4
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Solution
Verified by Toppr
Given
(
x
a
)
n
+
(
y
b
)
n
=
2
Differentiating both sides w.r.t
x
,
we get
n
a
(
x
a
)
n
−
1
+
b
b
(
y
b
)
n
−
1
×
d
y
d
x
=
0
⇒
d
y
d
x
=
−
n
a
(
x
a
)
n
−
1
×
b
a
(
b
y
)
n
−
1
∴
d
y
d
x
at
(
a
,
b
)
=
b
a
∴
Tangent is
y
−
b
=
−
b
a
(
x
−
a
)
⇒
b
x
+
a
y
=
2
a
b
⇒
x
a
+
y
b
=
2
for all values of
n
(
∵
d
y
d
x
is independent of
n
)
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Similar Questions
Q1
If the curve
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n
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(
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