Engineering Board Exam Reviewer · Curvature and Radius of Curvature · hard

Find the radius of curvature of the ellipse x=2 t, y= t at the point (2,0).

  1. 0.5
  2. 2
  3. 4
  4. 1

Answer

A. 0.5

Solution

At t=0: x'=-2 t=0, y'= t=1, x''=-2 t=-2, y''=- t=0. = |x'y''-y'x''|≤ft(x'2+y'2 )3/2=|0-(1)(-2)|/1=2, so R= 1 =0.5.

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