# Find the parameterization of the surface area given by #z = x^2 - 2x + y^2#?

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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