(b) The curvature k of a curve C at a given point is a measure of how quickly the curve changes direction at that point. For example, a straight line has curvature k = 0 at every point. For a curve C with parametric equations x = (x(t), y(t)) the curvature can be calculated by x(t), y = y(t), then at the point |a (t)y" (t) – 3' (t)a" (t)| (7'(t))? + (y'(t))?)³/2 K = Use your parametric equations from (a) to calculate the curvature of the ellipse at (x(t), y(t)).

(b) The curvature k of a curve C at a given point is a measure of how quickly the curve changes direction at that point. For example, a straight line has curvature k = 0 at every point. For a curve C with parametric equations x = (x(t), y(t)) the curvature can be calculated by x(t), y = y(t), then at the point |a (t)y" (t) – 3' (t)a" (t)| (7'(t))? + (y'(t))?)³/2 K = Use your parametric equations from (a) to calculate the curvature of the ellipse at (x(t), y(t)).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 53E

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