Find out what kind of conic section the following quadratic form represents and transfo

Ramsey 2020-12-05 Answered

Find out what kind of conic section the following quadratic form represents and transform it to principal axes. Express xT=[x1x2] in terms of the new coordinate vector yT=[y1y2]
x1212x1x2+x22=70

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ottcomn
Answered 2020-12-06 Author has 97 answers

Given quadratic equation is x1212x1x2+x22=70
The matrix representation of quadratic form is
image
Now trace (A)=2anddet(A)=35
Characteristic equation of matrix A is λ22λ35=0
Therefore eigen values of matrix A are λ=5,7
Since matrix A has both positive and negative eigen values, therefore matrix A is indefinite.
Given quadratic form is hyperbolic

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