The length of normal at any point to the curve, `y=c cosh(x/c)` is

Options

A. fixed
B. `1/(c^(2))`
C. c
D. `c^(2)`

Answer

C

Explanation

Given `y=c cos (x/c)`………..i
`implies(dy)/(dx)=- c . 1/c . sin (x/c)=-sin(x/c)`
Now, length of normal
`=ysqrt(1+((dy)/(dx))^(2))=c cos (x/c)sqrt(1-sin^(2)(x/c))`
At `x=0` length of normal
`=c cos (0/c)sqrt(1-sin^(2)(0/c))=cxxsqrt(1-0)=c`