rsst123
  • rsst123
*WILL MEDAL* A curve C has the parametrization x = a sint cosα , y = bsint sinα , z = c cost, t ≥ 0 where a, b, c, α are all positive constants a)Show that C lies on the ellipsoid x^2/a^2 +y^2/b^2+z^2/c^2=1 (b) Show that C also lies on a plane that contains the z-axis (c) Describe the curve C. Give its equation I understand how to get a , by replacing the values for x,y,and z, but I am having trouble how to explain b and c. can someone please help thank you!
Mathematics
katieb
  • katieb
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IrishBoy123
  • IrishBoy123
actually, that answer was not great. mea culpa! if you just do \(\vec r \times \ \vec t\) and you get the normal vector to the curve for all value of the parameter t, not just the 0 and \(\pi/2\) \(\vec r \times \ \vec t\) looks something like \(<-cb \ sin\alpha, ac \ cos\alpha, 0>\), ie no \(\hat z\) component meaning that z axis is in the plane itself..... :p

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