Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be the image of σ. (1) Show that S is a ruled surface. (2) Give a quadratic equation for S, and show S is a quadric. (3) Show tha...
Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be the image of σ. (1) Show that S is a ruled surface. (2) Give a quadratic equation for S, and show S is a quadric. (3) Show that S is an elliptic cylinder, so that a cross section of S perpendicular to the rulings is an ellipse. What are the lengths of its axes?
Question 2. Define σ: R2-R by σ(u,t)-(u+cosu, sinu, u), and let S be the image of σ. (1) Show that S is a ruled surface. (2) Give a quadratic equation for S, and show S is a quadric. (3) Show that S is an elliptic cylinder, so that a cross section of S perpendicular to the rulings is an ellipse. What are the lengths of its axes?