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Which standard equation represents an ellipse?

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Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated.
analytic geometry The conic sections result from intersecting a plane with a double cone, as shown in the figure. There are three distinct families of conic sections: the ellipse (including the circle), the parabola (with one branch), and the hyperbola (with two branches).

In analytic geometry, the standard equation for an ellipse centered at the origin with its axes aligned with the x and y axes is:

x2a2+y2b2=1

In this equation, the length of the major diameter is 2a and the length of the minor diameter is 2b.1