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Byju's Answer
Standard XII
Mathematics
Equation of Tangent at a Point (x,y) in Terms of f'(x)
The equation ...
Question
The equation of tangent to the curve
(
x
a
)
n
+
(
y
b
)
n
=
2
at the point
(
a
,
b
)
is
A
x
a
=
−
y
b
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B
x
a
+
y
b
=
2
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C
x
2
a
2
−
y
2
b
2
=
n
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D
x
a
=
y
b
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Solution
The correct option is
B
x
a
+
y
b
=
2
Given equation of the curve,
(
x
a
)
n
+
(
y
b
)
n
=
2
Differente the above equation to find the slope of the curve
n
(
x
a
)
n
−
1
.
1
a
+
n
(
y
b
)
n
−
1
.
1
b
d
y
d
x
=
0
⟹
d
y
d
x
=
−
b
a
(
x
a
)
n
−
1
(
b
y
)
n
−
1
∴
Slope at
(
a
,
b
)
=
−
b
a
(
a
a
)
n
−
1
(
b
b
)
n
−
1
=
−
b
a
∴
Equation of the tangent at
(
a
,
b
)
is:
(
y
−
b
)
=
−
b
a
(
x
−
a
)
b
x
+
a
y
=
2
a
b
x
a
+
y
b
=
2
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0
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Standard XII Mathematics
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