Working on this problem and one of my classmates tried substituting x and y in terms on (z,theta) and once solved 1=1. Does that prove that it is a ruled surface?

Thank you

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- April 29th 2013, 01:32 PMtopsaaRuled surface calculus
Working on this problem and one of my classmates tried substituting x and y in terms on (z,theta) and once solved 1=1. Does that prove that it is a ruled surface?

Thank you - April 29th 2013, 10:48 PMchiroRe: Ruled surface calculus
Hey topsaa.

Can you show us what you tried (and how you got 1=1)?

One hint that I can think of is to take the line equation, break up the functions and square all elements and try re-arrange them to show that you get x^2 + y^2 - z^2 = 1 which proves that the line lies on the surface. - April 29th 2013, 11:11 PMtopsaaRe: Ruled surface calculus
x^2 + y^2 - z^2 = 1

replaced x= zsin(theta) + cos(theta), y=-zsincos(theta) + sin(theta)

when plugging them in I get z^2 - z^2 + 1 = 1 , so 1 = 1