Section 11.7 #16

Let , , and :

> x:=sin(t);y:=cos(t);z:=sin(t)^2;

Now let's see if these correspond to the intersection of the circular cylinder and the parabolic cylinder :

> x^2+y^2;

> simplify(%);

> z-x^2;

Indeed, we see that the space curve is the intersection of the two cylinders.

Let's plot these cylinders so we can visualize their intersection:

Plotting the circular cylinder

Plotting the parabolic cylinder

Putting the two cylinders on the same plot

Plotting the space curve of intersection

Putting the two cylinders and the space curve on the same plot