The equation x2 - xy + y2  =3 represents a “rotatedellipse,” that is, an ellipse whose axes are not parallel to the coordinate axes. Find the points at which this ellipsecrosses the -axis and show that the tangent lines at thesepoints are parallel.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 45E
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The equation x2 - xy + y2  =3 represents a “rotated
ellipse,” that is, an ellipse whose axes are not parallel to the coordinate axes. Find the points at which this ellipse
crosses the -axis and show that the tangent lines at these
points are parallel.

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