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Mathematics-Online problems:

Interactive Problem 501: Conic Section

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
#./interaufg501_en.tex#Given the conic section $ \ 5x^2 + 6xy + 5y^2 = 8\ . $
a)
Give the normal form of the conic section. What kind of curve is it?

b)
Find the principal axes of the conic section.

c)
Give a sketch of the conic section in the $ xy$ - plane.

Solution:

a)
Eigenvalues:      $ \lambda_1=$,          $ \lambda_2=$        ( $ \lambda_1<\lambda_2$).

Normal Form:      $ \displaystyle \frac{u^2}{a^2}\pm\frac{v^2}{b^2}=1$         $ a=$,     $ b=$,          n/a     $ +$     $ -$ .

Type:     n/a,         Ellipse ,          Hyperbola

b)
Direction of the principal axes $ u$ and $ v$:     $ ($,$ -1)^t$     and     $ ($,$ 1)^t$
c)

  n/a    
       

\includegraphics[bb=116 460 330 660,clip,height=0.3\linewidth]{P11_3_Bild4}

\includegraphics[bb=116 460 330 660,clip,height=0.3\linewidth]{P11_3_Bild2}

\includegraphics[bb=116 460 330 660,clip,height=0.3\linewidth]{P11_3_Bild3}

\includegraphics[bb=116 460 330 660,clip,height=0.3\linewidth]{P11_3_Bild1}

   
(Authors: Höllig/Höfert)

see also:

  automatically generated: 3/12/2018