- #1
Stevecgz
- 68
- 0
Question: Consider the intersection of the paraboloid [tex]z = x^2 + y^2[/tex] with the plane [tex]x - 2y = 0[/tex]. Find a parametrization of the curve of intersection and verify that it lies in each surface.
How I went about it:
[tex]x = 2y[/tex]
[tex]z = (2y)^2 + y^2 = 5y^2[/tex]
Set [tex]y = t[/tex], then
[tex]x = 2t[/tex]
[tex]y = t[/tex]
[tex]z = 5t^2[/tex]
I don't know that my answer is wrong, I'm just not certain if I am going about it the correct way. If someone could let me know I would appreciate it. Thanks.
Steve
How I went about it:
[tex]x = 2y[/tex]
[tex]z = (2y)^2 + y^2 = 5y^2[/tex]
Set [tex]y = t[/tex], then
[tex]x = 2t[/tex]
[tex]y = t[/tex]
[tex]z = 5t^2[/tex]
I don't know that my answer is wrong, I'm just not certain if I am going about it the correct way. If someone could let me know I would appreciate it. Thanks.
Steve