Finding Axes of Conic Section Equation

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aamirnshah
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Hi,

I've been stuck on this for a few days now.

I am trying to determine the X and Y axis of the general conic section equation:

Q(x,y)=Ax^2 +Bxy+Cy^2 +Dx+ Ey+F =0

I have A, B, C, D, E, and F.

I have already determined the center coordinates, but I have not found information on how to find the two minor and major axes of the equations.

Any help is appreciated. Thanks

AS
 
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Welcome to PF!

Hi aamirnshah! Welcome to PF! :smile:

They'll be the eigenvectors of the matrix (A B/2; B/2 C).

Alternatively, just apply the formula for rotating coordinates through a particular angle to the original equation so as to produce an xy term of zero. :wink:
 


tiny-tim said:
Hi aamirnshah! Welcome to PF! :smile:

They'll be the eigenvectors of the matrix (A B/2; B/2 C).

Alternatively, just apply the formula for rotating coordinates through a particular angle to the original equation so as to produce an xy term of zero. :wink:

Wow thanks for the quick reply. So I have obtained the eigenvector of the matrix (A B/2; B/2 C). From my research I have determined that I also need to determine the eigenvalues of that matrix. But from here, I am still confused. How does this relate to knowing the 'a' and the 'b' in the equation:

x^2 / a^2 - y^2 / b^2 = 1
 
aamirnshah said:
From my research I have determined that I also need to determine the eigenvalues of that matrix. But from here, I am still confused. How does this relate to knowing the 'a' and the 'b' in the equation:

x^2 / a^2 - y^2 / b^2 = 1

Hint: what are the eigenvalues associated with x2/a2 - y2/b2 = 1? :wink:
 

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