# Question about parameterizing curve of intersection.

 P: 122 I couldn't find any resources in my book or online dedicated to this subject. I honestly don't even know where to begin for this problem. 1. The problem statement, all variables and given/known data Let $f(x,y) = 4 / (1+ x^2 + y^2)$ and let S be the surface given by the graph of f(x,y) b) Let C2 denote the curve in the xy-plane given by $r(t)= t, 3/2 − t^2$ and let C denote the curve on the surface S which has C2 as its shadow in the xy-plane. Find the parametric equations r = r(t) for C 2. Relevant equations 3. The attempt at a solution
 P: 428 how about the "graph" over the curve, $$(r(t),f(r(t))=(x(t),y(t),z(x(t),y(t)))$$ Then it is a curve, on the surface, and it's shadow is r(t), correct?
 P: 122 I dont deal well with this sort of abstraction. In my mind what you are saying is we can come up with a new function which is simply our old function r(t) plus a new variable which is the sum of the variables of our original function. Correct me if I am wrong. But it would appear to me that we need our original function to come up with the parameters, since S is the measure of the surface of $f(x,y)=4/(1+x2+y2)$. Oh and one last thing. A "shadow" is simply a projection correct?