Question

The radius of curvature at the point (S,Y ) on the
curve 5=c log sec y is​

Answer 1

The radius of curvature is c tanψ

Step-by-step explanation:

Given,

s = c log(secψ)

Now, differentiating with respect to ψ, we get

ds/dψ = d/dψ {c log(secψ)}

= c d/dψ {log(secψ)}

= c * 1/secψ * d/dψ (secψ)

= c * 1/secψ * secψ tanψ

= c tanψ

Therefore the radius of curvature is

ρ = ds/dψ = c tanψ .

Problem:

1. Find the radius of curvature at the point (s, ψ) of the curve s = a secψ tanψ + a log(secψ + tanψ).

2. Find the radius of curvature of y = x e⁻ˣ at a point where y is maximum.