sketch Curve

[steller]

Show that the curve with vector equation \(\displaystyle r(t)=<2cos^2t,sin(2t), 2sint>\)
is the curve of intersection of the surfaces

and

. Use this fact to sketch the curve.

First, i was able to solve the problem. answer 1=1

The teacher said we could use a graphing program to sketch the curve.
do i just sketch the vector equation?
would i sketch

\(\displaystyle y^2 = 1 - (x-1)^2\)

 

[DrPhil]

Show that the curve with vector equation \(\displaystyle r(t)=<2cos^2t,sin(2t), 2sint>\)
is the curve of intersection of the surfaces

and

. Use this fact to sketch the curve.

First, i was able to solve the problem. answer 1=1

The teacher said we could use a graphing program to sketch the curve.
do i just sketch the vector equation?
would i sketch

\(\displaystyle y^2 = 1 - (x-1)^2\)

To "sketch" the curve based on the fact that it is the intersection of two surfaces, you would sketch the two surfaces and estimate where they intersect.
First surface is a ____ parallel to the ___ axis, centered at ___, ___, with radius ___
Second surface is a ____ centered at ___, ___, ___, and with radius ___.
[I envision two inclined ellipses, touching at one point. Lots of symmetry.]

If you use a graphics program, enter the vector equation.