Find the parameterization of the surface area given by #z = x^2 - 2x + y^2#?
A possible parameterization is # **r**(p, q) = (1 + p * cos(q), p sin(q), p^2 - 1)# , but why?
A possible parameterization is
1 Answer
Jul 19, 2018
Looking at your suggested parameterization, rather than actually finding one:
#bb r (p, q) = (:underbrace(1 + p cos(q))_(=x(p,q)),underbrace( p sin(q))\_(=y(p,q)), underbrace(p^2 - 1)\_(=z(p,q)) :)#
Looking at individual terms of
#{(x^2 = 1 + 2 p cosq + p^2 cos^2 q , qquad bbb(A)) ,(- 2x = -2 - 2 p cosq , qquad bbb(B)), (y^2 = p^2 sin^2q , qquad bbb(C) ):}#
So that seems to work