Mathematik-Online problems: Problem 65: Section of Quadrics and Planes

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	Mathematik-Online problems:
	Problem 65: Section of Quadrics and Planes

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

Let $Q:\, 2x_1^2 +2 x_2^2 - x_3^2 = 0$ be a quadric in $\mathbb{R}^3$ .

a)

Show that

defines a double cone.

b)

Analyse what kind of geometric figures are the results of the section of

and the following planes:

$\displaystyle \begin{array}{ll} E_1:\ x_1=1 & E_2:\ \sqrt{2}\,x_2+x_3=1 \\ [0.4cm] E_3: \ x_1+2x_3=-1 \quad & E_4: \ x_1-x_2=0 \end{array}$

c)

Find a plane whose section with

is a circle of radius 2.

d)

Do planes exist whose section with

is a line?

(Authors: Kimmerle/Apprich/Höfert)

Solution:

automatisch erstellt am 14. 12. 2007