Thread: Parametrization of the intersection of cylinders

Use sine and cosine to parametrize the intersection of the cylinders x^2+y^2=1 and x^2+z^2=1 (use two vector-valued functions). Then describe the projections of this curve on the three coordinate planes.

I am not sure how to do this problem at all any help would be great. Thanks

Originally Posted by acasas4

Use sine and cosine to parametrize the intersection of the cylinders x^2+y^2=1 and x^2+z^2=1 (use two vector-valued functions). Then describe the projections of this curve on the three coordinate planes.

I am not sure how to do this problem at all any help would be great. Thanks

The projection of the cylinder on the Oxy-plane is a circle , which has this parametric equation

Also

So,

See the plot, where
- the blue line is
- the red line is



For Maple

with(plots):
A := spacecurve([cos(t), sin(t), sqrt(1-cos(t)^2)], t = 0..2*Pi, color=red, thickness=3):
B := spacecurve([cos(t), sin(t), -sqrt(1-cos(t)^2)], t = 0..2*Pi, color=blue, thickness=3):
display(A, B, axes=normal, scaling=constrained, view=[-2..2, -2..2, -2..2], numpoints=1000);