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The equation $ x^2 - xy + y^2 = 3 $ represents a "rotated ellipse," that is, an ellipse whose axes are not parallel to the coordinates axes. Find the points at which this ellipse crosses the $ a-axis $ and show that the tangent lines at these points are parallel.

crosses at $( \pm \sqrt{3}, 0)$ and both tangents have slope 2

01:34

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Mtro. C.

July 29, 2021

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