Help!!! Need some math help - Fairly advanced stuff so come strutt your stuff an help me out :)

[shikhan]

Find a vector function that represents the curve of intersection of the two surfaces:

1) The cone z= sqrt(x^2 + y^2) and the plane z=1+y

2) The paraboloid z=4x^2 + y^2 and the parabolic cylinder y=x^2


I do have the anser to number 1 from the back of the book, but i need to know how to do it and the example problem in the book basically told me this: Find the intersection, change into paramatric equations for x, y , z, bam, you have an answer.... I'm not sure how to do the first two steps...

Bah... help, please!!!

edit: spelling

 

[janlievens]

z2 = x2 + y2; (1)
z=1+y; (2)
solution:
(2) => z2 = 1 + 2y +y2; (3)
(1) = (3) => 1 + 2y = x2 (4)

the intersection is described by (4) and (2)

=>

x = sqrt ( 1 + 2t );
y = t;
z = 1 + t;

=>

Fxyz ( t ) = ( sqrt( 1 + 2t) , t , 1 + t );

 

[shikhan]

Blah, the example problem made it look alot harder than that [they used trig but when check with the answers... these are equivilent.. .grr]


so is this right for part 2?


z=4x^2 + y^2
y=x^2

x=t
y=t^2
z=4t^2+t^4


v = <t, t^2, 4t^2+t^4>


?

Arg, if it is that easy, i'm gonna kill myself for thinking that doing it that was was too easy for a question in this course...

 

[janlievens]

Yep, that's the correct answer!

Clearly this is not "Fairly advanced stuff".

Arg, if it is that easy, i'm gonna kill myself for thinking that doing it that was was too easy for a question in this course...
NO....PLEASE DON'T DO THAT ! ! ! ! !

 

[shikhan]

Nope... apparently its not fairly advanced stuff... It was just teh way the book worded it and the fact that i'm supposed to be doing MVC.... stupid me eh? Oi, live an learn...

I'll try to have a higher caliber / harder problem next time i ask, promise!

Arg, if it is that easy, i'm gonna kill myself for thinking that doing it that was was too easy for a question in this course...
NO....PLEASE DON'T DO THAT ! ! ! ! !

Eh.... just really mad at myself for not seeing such a simple solution to the problem. I mean... how stupid can a guy get eh?