The graph of the equation
is an ellipse lying obliquely in the plane,
as illustrated in the figure
below.
a.
Compute .
.
b.
The ellipse has two horizontal tangents.
Find an equation of the lower one.
The lower horizontal tangent line is
defined by the equation
.
c.
The ellipse has two vertical tangents.
Find an equation of the rightmost one.
The rightmost vertical tangent line is
defined by the equation
.
d.
Find 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 .
To find the vertical tangent use symmetry, or solve
.
You can earn partial credit on this problem.