find the length of normal and subnormal of the curve y al (e x/a+e -x/a) at any point
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Class 12
>>Maths
>>Application of Derivatives
>>Tangents and Normals
>>Length of the normal to the curve at any
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Length of the normal to the curve at any point on the curve y=
2
a(e
x/a
+e
−x/a
)
varies as
Medium
Solution
verified
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Correct option is D)
Given,
y=
2
a(e
a
x
+e
−
a
x
)
⇒y=acosh(
a
x
)
dx
dy
=asinh(
a
x
)
a
1
=sinh(
a
x
)
Length of normal =y[1+(
dx
dy
)
2
]
2
1
=acosh(
a
x
)[1+sin
2
h(
a
x
)]
2
1
=acosh(
a
x
)[cos
2
h(
a
x
)]
2
1
=acos
2
h(
a
x
)
=a×
a
2
y
2
=
a
y
2
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