Question

CURVATUREFor the curve : s^2= 8ay, show that p =4a√[1-y/2a) [Kanpur B.Sc.Prove that the curvature at a point of the​

Answer 1

Answer:

s^2= 8ay

differentiation

2s ds/dy=8a

2s cosec(Shai)=8a

Shai is a angle sign here I am writing it with the sign 't'

s=4a Sint

differentiation with respect t

ds/dt =4a cost. (ds/dt=curvature radius)

= 4a√{1-s^2/16a^2}

radius =4a √{1-y/2a}

here is your curvature radius

Answer 2

Answer:

There are two important types of curvature: extrinsic curvature and intrinsic curvature.

Step-by-step explanation:

The rate of change of direction of a curve with respect to distance along the curve.

$s^{2}$ = 8ay

Differentiation

2s ds/dy=8a

2s cosec(Sin t) = 8a

The curvature of a curve is, roughly speaking, the rate at which that curve is turning. Since the tangent line or the velocity vector shows the direction of the curve, this means that the curvature is, roughly, the rate at which the tangent line or velocity vector is turning.

This is a angle sign here I am writing it with the sign 't'

s = 4a Sin t

Differentiation with respect t,

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature.

ds/dt = 4a cost. (ds/dt=curvature radius)

         = 4a√{1-s^2/16a^2}

radius =4a √{1-y/2a}

Hence Proved

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