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## Homework Statement

Given the ellipse

##0.084x^2 − 0.079xy + 0.107y^2 = 1 ##

Find the semi-major and semi-minor axes of this ellipse, and a unit vector in the

direction of each axis.

I have calculated the semi-major and minor axes, I am just stuck on the final part.

## Homework Equations

this is where ##ux^2+2vxy+wy^2=1##

## The Attempt at a Solution

I have calculated the two eigenvalues, 0.13664... and 0.05436... and therefore found the semi-major and semi-minor axes. I'm just not sure where to go next. I have worked out the ratios for q/p but I'm not sure how to use them.