Question

Write the parametric formula for radius of curvature

Answer 1

Step-by-step explanation:

If a curve is given by the polar equation r=r(θ), the curvature is calculated by the formula. K=∣∣r2+2(r′)2−rr′′∣∣[r2+(r′)2]32. The radius of curvature of a curve at a point M(x,y) is called the inverse of the curvature K of the curve at this point: R=1K.

Answer 2

The radius of curvature is defined as the reciprocal of the curvature at any point of the given curve.

• The parametric form is that form that has an independent and dependent variable.
• while calculating the radius of curvature in the parametric form we have the formula

                 ρ =(x'² +y'²)³/₂ /x'y'' - y'x''

• In the given formula, x' represents the first-order derivative of x and y' represents the first-order derivative of y.
• x'' is represented by the second-order derivative of x and y'' represents the second-order derivative of y.