The graph of the equation x^2+xy+y^2=5 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 y= c) The ellipse has two vertical tangents. Find an equation of the rightmost one. The rightmost vertical tangent line is defined by the equation x= d)ind the point at which the rightmost vertical tangent line touches the ellipse. The rightmost vertical tangent line touches the ellipse at the point
Question: The graph of the equation x^2+xy+y^2=5 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 y=
c) The ellipse has two vertical tangents. Find an equation of the rightmost one. The rightmost vertical tangent line is defined by the equation x=
d)ind the point at which the rightmost vertical tangent line touches the ellipse. The rightmost vertical tangent line touches the ellipse at the point
Hint: The horizontal tangent is of course characterized by dy/dx=0. To find the vertical tangent use symmetry, or solve dx/dy=0.
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