# 21.5 The Ellipse

**Foci • Vertices • Major Axis • Minor Axis • Standard Equation – Axis along**`x`-axis • Standard Equation – Axis along`y`-axis • Calculator Display

The next important curve is the ellipse. *An* **ellipse** *is defined as the locus of a point P(x, y) that moves so that the sum of its distances from two fixed points is constant. These fixed points are the* **foci** *of the ellipse*. Letting this sum of distances be 2`a` and the foci be the points $(\hspace{0.17em}-\hspace{0.17em}c\hspace{0.17em},\hspace{0.17em}\text{}0)$ and (`c`, 0), we have

See Fig. 21.57. The ellipse has its center at the origin such that `c` is the length of the line segment from the center to a focus. We will also see that `a` has a special meaning. Now, from Section 14.4, we see that we should move ...

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