The graph of the equation x + xy+ y = 8 is an ellipse lying obliquely in the plane, as illustrated in the figure below. dy a. Compute dx dy dx 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 = 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 = 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 dy Hint: The horizontal tangent is of course characterized by = 0. To find the vertical tangent use symmetry, or solve = 0. dx
The graph of the equation x + xy+ y = 8 is an ellipse lying obliquely in the plane, as illustrated in the figure below. dy a. Compute dx dy dx 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 = 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 = 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 dy Hint: The horizontal tangent is of course characterized by = 0. To find the vertical tangent use symmetry, or solve = 0. dx
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter12: Conic Sections
Section12.2: Ellipses
Problem 64E: How Wide Is an Ellipse at a Focus? A latus rectum for an ellipse is a line segment perpendicular to...
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The graph of the equation ?^2+??+?^2=8 is an ellipse lying obliquely in the plane, as illustrated in the figure below.
a.Compute dy/dx
b.The ellipse has two horizontal tangents. Find an equation of the upper one.
The upper horizontal tangent line is defined by the equation ?=
c.The ellipse has two vertical tangents. Find an equation of the leftmost one.
The leftmost vertical tangent line is defined by the equation ?=
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
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