The equation x2 − xy + y2 = 3 represents a “rotated ellipse”, that is an ellipse whose axes are not parallel to the coordinate axes. (a) Find the points at which this ellipse crosses the x - axis and show that the tangent lines at these points are parallel (b) Where does the perpendicular line to this ellipse at the point (-1,1) intersect the ellipse a second time?

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