Name
Math 210
Quiz #3
Sec. 13.1-13.2 September 15, 2009
You must show all of your work to receive full credit. Please put a box around
the final answer.
Find a parametrization of the intersection of the surfaces
y2−z2=x−2 and y2+z2= 9
using y=tas a parameter.
Solving both surfaces for z2we find that
z2=y2−x+ 2 and z2= 9 −y2.
We set the equations equal to each other
y2−x+ 2 = 9 −y2
and solve for x
x= 2y2−7.
From y2+z2= 9 we can see that z=±p9−y2.
Letting y=tbe the parameter, we find that surfaces intersect at
~r(t) =<2t2−7, t, ±√9−t2>, where −3≤t≤3.
