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The graph of the equation x² + xy + y² = 4 is an ellipse lying obliquely in the plane, as illustrated in the figure below. Y X

The graph of the equation x² + xy + y² = 4 is an ellipse lying obliquely in the plane, as illustrated in the figure below. Y X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please check if my answers to part a.b.c.d are correct. thanks!

The graph of the equation x² + xy + y² = 4 is an ellipse lying obliquely in the plane, as illustrated in the figure below. Y X
Transcribed Image Text:The graph of the equation x² + xy + y² = 4 is an ellipse lying obliquely in the plane, as illustrated in the figure below. Y X
a. Compute dy dx = dy dx -(2x+y)/x+2y b. The ellipse has two horizontal tangents. Find an equation of the upper one. The upper horizontal tangent line is defined by the equation y = 4/sqrt(5) c. The ellipse has two vertical tangents. Find an equation of the leftmost one. The leftmost vertical tangent line is defined by the equation x = -2/sqrt(5) d. Find the point at which the leftmost vertical tangent line touches the ellipse. The leftmost vertical tangent line touches the ellipse at the point -2/sqrt(5),-2
Transcribed Image Text:a. Compute dy dx = dy dx -(2x+y)/x+2y b. The ellipse has two horizontal tangents. Find an equation of the upper one. The upper horizontal tangent line is defined by the equation y = 4/sqrt(5) c. The ellipse has two vertical tangents. Find an equation of the leftmost one. The leftmost vertical tangent line is defined by the equation x = -2/sqrt(5) d. Find the point at which the leftmost vertical tangent line touches the ellipse. The leftmost vertical tangent line touches the ellipse at the point -2/sqrt(5),-2
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