Ellipse Symmetry at the Origin

An ellipse centered at the origin shows clear symmetry in its graph. Its equation describes a smooth, closed curve whose distance from the center keeps a constant ratio between the horizontal and vertical axes. Because the ellipse stretches farther along the x-axis than the y-axis, it has a horizontal shape.

The equation of an ellipse centered at the origin represents a shape in which every point on the curve is at a constant sum of distances from two points called foci, and every point has a symmetric match across the axes.

Like an elliptical planetary orbit, this ellipse forms a smooth curve stretching farther along the x...