For the first two, show that and calculate . The third one is but an easy problem involving analytic geometry only. For the fourth one, call the coordinates x and y,
and calculate an algebraic expression involving them.
Suppose that is the parametrised curve given by
=
for .
- Show that is parametrised by arc length.
- Find the length of .
- Find the normal vector to (t0) at where .
- Do you recognise this curve?
I don't have a clue what any of this means, the lecturer rushed through it and I won't have a chance to see her until Tuesday and this is in for Monday. Any help is much appreciated. Thanks.