Homework 2
Instructions: The following homework set contains 2 problems. Solve each problem
on a separate page. Scan or take a photo of your solution to each problem and submit it
corresponding assignment on Brightspace before the deadline.
Explain your work. Arguments without proper explanation might get reduced or no credit.
(1) A particle moves along the curve Γ of the intersection of surfaces z 2 = 12y and
18x = yz in the upward direction.
(a) Write a parametric equation for Γ using t = z/6 as a parameter.
(b) Find the length of Γ from (0, 0, 0) to (1, 3, 6).
(2) Consider the plane curve C given by the parametrization
⃗r(t) = cosh(t)⃗i + sinh(t)⃗j
Notice that t is not the arclength parameter and the curve passes through (1, 0) at
t = 0.
(a) (4 pts) Compute the curvature of C at (1, 0).
⃗ at (1, 0).
(b) (4 pts) Compute principal unit normal vector N
(c) (2 pts) Find the center and the radius of the osculating circle of C at (1, 0).