Homework 2 MATH162-24 Calculus

KOREA UNIVERSITY
MATH162-24
HW#2 Solutions


1. [4 points] Find a vector function that represents the curve of intersection
of the two surfaces:
The hyperboloid      and the cylinder      .


(Solution)




2. [4 points] Find a vector equation for the tangent line to the curve of
intersection of the cylinder
     and      at the point     .
(Solution)




3. [4 points] Find equations of the osculating circles of the ellipse
     at the point    .

(Solution)
Let   cos    sin  to describe the parametric equation of the ellipse.
Then     cos  sin   ′    sin  cos   and
″    cos   sin   and
 ′      sin  cos     
 sin    cos