find the parametric equation of the following curve:
ellipse x^2+y^2=1 , z=y

Question

find the parametric equation of the following curve:
ellipse x^2+y^2=1 , z=y

loser66 · Answer

I have question: is x^2 + y^2 =1 an ellipse? is it not a circle?

anonymous · Answer

no its written as ellipse in the qst

anonymous · Answer

x^2 + y^2 =1 is a circle. Look: https://www.wolframalpha.com/input/?i=x%C2%B2%2By%C2%B2%3D1&lk=4&num=2

loser66 · Answer

@IgorL I think so, too. but you see, he answered that is an ellipse. Whatever, we have to find out the parametric equation for that, (anyway, circle is  a special case of ellipse) . I stuck at z = y and try to find out the parametric for that part.

experimentx · Answer

x = y => x(t) = t, y(t) = t

anonymous · Answer

ok

loser66 · Answer

@experimentX no, z = y not x =y

loser66 · Answer

x = cos t and y = sin t

experimentx · Answer

if you are considering 3d space,  x^2+y^2=1 , z=y is not a curve anymore, it's a region

loser66 · Answer

yes, I need the pic, too. please, draw it out

loser66 · Answer

@experimentX can we solve it by algebraic way only?

experimentx · Answer

woops!! it's a curve ... sorry

experimentx · Answer

i misinterpreted, it's an ellipse indeed

loser66 · Answer

:) don't get

experimentx · Answer

x^2+y^2 = 1 is a cylinder and x=z is a plane, when a cylinder intersects plane what do you get?

loser66 · Answer

nope, sorry, ellipse only

experimentx · Answer

no  ... it's an ellipse.|dw:1368024664946:dw|