 Solution

ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2011/3/c/i/solution

Differentiate to get

r_{u} = (a cos v, a sin v, 0), r_{v} = (- a u sin v, a u cos v, 1) .

Their squared lengths are

a^{2}

and

a^{2} u^{2} + 1

I = a^{2} d u^{2} + (a^{2} u^{2} + 1) d v^{2} .

 New to topics? Read the docs here!