- #26

Dick

Science Advisor

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You could look at your expansion to find a relation between A and C. What is it? But you could also determine that just by looking at the matrix you are taking the determinant of and figuring what factors multiply ##x_1^2## and ##x_2^2##. Think about expansion by minors. Once you've figured out what kind of conic you have - you still need to know some points it passes through to determine the conic. That's a separate issue - but again there's an obvious answer by staring at the unexpanded determinant.Okay, so the equation becomes:

##Ax_1^2+Cx_2^2+Dx_1+Ex_2+F=0##

I found this online

##B^2 - 4AC > 0##, hyperbola

##B^2 - 4AC = 0##, parabola

##B^2 - 4AC < 0##, ellipse or circle (circle only if B = 0 and A = C)

B=0, so we have to find A&C, to determine the form of the conic section.

So the other constants are combinations of a's, b's, and c's. Would I need to look have to look at the expanded form of the determinant to match the corresponding coefficients or is thinking of which points on a conic a method that will lead me to the same solution, but in a much easier way?