find the length of normal and sub normal to the curve y=a/2(e^x/a+e^-x/a) at any point
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Medium
Answer
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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