I am stuck on this calc problem, and need massassi's help!

Consider the paraboloid z=x^2+y^2. The plane 4x-7y+z=0 cuts the paraboloid, its intersection being a curve.
Find "the natural" parametrization of this curve.
Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface.

c(t)=(x(t), y(t), z(t)) where,
x(t)=?
y(t)=?
z(t)=?


I'm pretty sure I have to find the circle projected by the curve on the xy plane, then use that to find the curve itself, but I'm not sure what to do to get that.

Don't worry, I managed to figure it out. The first time I tried it I did the right thing, but had made a simple algebra mistake when completing the square. Problem solved

Guh? O_o

I gave up at paraboloid.

yeah i'm still considering it

heh, parametrization is basically making an equation look different. Such as making it use 't' instead of 'x'
By parametrizing it with the variable 't' I wrote an equation for the x-y-z coordinates of the curve with respect to 't'.

if you're still unsure what it means and you really want to know, then think of it this way, you have the equation y=5x
in parametric form, that would be y=5t, x=t. congratulations, you just parametrized with the variable 't'

if you still don't know what I'm talking about, then this is either way beyond what you should be learning anyway, or it's been so long since you did anything with math that it doesn't even matter.




[edit] oh and parabaloids are a type of 3 dimentional figures. if you want to know more about them, look it up on google and see the pretty pictures [/edit]