How do i find the orthogonal projection of a curve?

[kiwilava]

Homework Statement

curve S is the intersections of two surfaces, i have to find the curve obtained as the orthogonal projection of the curve S in the yz-plane

Homework Equations

how do i find the orthogonal projection of curve S??

The Attempt at a Solution

i found the equation of curve S to be (y-1)^2+(z+2)^2=5
and i know that orth_ab=b-proj_ab, where a and b are vectors

 

[Dick]

(y-1)^2+(z+2)^2=5 doesn't describe a curve. It's cylindrical surface. How did you get that by intersecting two other surfaces?

 

[kiwilava]

the two surfaces are x=y^2+z^2 and x-2y+4z=0, i substituted x in the second equation.. is that correct?

 

[Dick]

Not really, if you want to get a curve. f(x,y,z)=C doesn't generally describe a curve. It's still a surface. On the other hand you did the right thing. Projecting an intersection of two surfaces to the yz plane just means eliminating x. Your expression in terms of y and z is already the correct curve in the yz plane.

 

[kiwilava]

do you know how i can find the curve obtained as the orthogonal projection of the curve S in the yz-plane? or did i already find the answer?

 

[Dick]

You already found the answer. If you have an (x,y,z) point on the curve then the projection to the yz plane is (y,z). That just means you take your two surface equations and eliminate x. What could be wrong with that?

 

[kiwilava]

Oh i see, thanks for your help! ^_^