Question: A concho-spiral

A concho-spiral is a curve C that has a parametrization :

x=a(e)^mu(t)*cos(t)

y=a(e)^mu(t)*sin(t)

z=b(e)^mu(t)

t>=0

where a, b, mu, are constants.

  1. Show that C lies on the cone a^2*z^2=b^2*(x^2+y^2).
  2. Sketch C for a = b = 4 and mu=-1.
  3. Find the length of C corresponding to the t-interval [0,infinity].
Please Wait...