In Problem, identify the graph of each equation without completing the squares.
The equation represents graph of an ellipse.
An equation is .
The equation where and both cannot be zero,
(a) Defines a parabola if .
(b) Defines an ellipse (or a circle) if .
(c) Defines a hyperbola if
Comparing the given equation with the equation we can see that and So, we get .
Since , the given equation is the equation of an ellipse.
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