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Mathematik-Online problems:

Problem 73: Analysis of a Hyperbolic Cylinder

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given the hyperbolic cylinder

$\displaystyle {\cal{Z}}: 3x_1^2-x_2^2+3x_3^2+6x_1x_3+1=0 $

in $ \mathbb{R}^3$ .
a)
Find the asymptotic plane of $ {\cal{Z}}$ .
b)
Find the intersections of $ {\cal{Z}}$ and the line

$\displaystyle g: x=\left(\begin{array}{r}3\\ 3\\ 1\end{array}\right)+t\left(\begin{array}{r}-1\\ 2\\ 1\end{array}\right). $

c)
Show that the plane $ E: 12x_1-7x_2+12x_3+1=0$ is tangential to $ {\cal{Z}}$ and find the corresponding boundary line.

(Authors: Apprich/Knödler/Höfert)

see also:

  automatisch erstellt am 14. 12. 2007