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## Homework Statement

Find the equation of the line perpendicular to the ellipse x^2 − xy + y^2 = 3 at the point (-1,1). Where does the perpendicular line intercept the ellipse a second time?

## Homework Equations

???

## The Attempt at a Solution

I have already found the equation of the perpendicular line (f(x) = x - 2), just not sure how prove mathematically where it intercepts again. Of course I can just look at the graph, but I should be able to do it without referring to the graph at all. The slope of the line BTW is -1.