Hey guys... Have a Diff Geometry exam coming up and looking at the past papers this keeps coming up but I cant get my head around it! Can anyone help......

Sample Question

Q: The plane through a point on a curve г c R^3 perpendicular to the tangent line is called the normal plane to the curve at the point.

(a)Show that a curve lies in a sphere if the intersection of all normal planes is non-empty.

(b)Hence, or otherwise show that the curve parametrized by

P(ө) = (cos 2ө, -2cosө, sin2ө), ө is an element of [0, 2*Pi] lies in a sphere. Find the centre and radius of the sphere!

AGH!

From a Confused Student...