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
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
