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

Ramsey

Ramsey

Answered question

2020-12-05

Discover which type of conic section the following quadratic form represents and change it to principal axes. Express xT=[x1x2] in terms of the new coordinate vector yT=[y1y2]
x1212x1x2+x22=70

Answer & Explanation

ottcomn

ottcomn

Skilled2020-12-06Added 97 answers

The quadratic equation is x1212x1x2+x22=70
The matrix representation of quadratic form is
image
Now follow (A)=2 and det(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 not definite.
Given quadratic form is hyperbolic

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