Sketching Ellipses

Setting x = 0 we see that the ellipse meets the y-axis at the two points y = ±b. Also, it meets the x-axis at x = ±a. Since all terms are ≥ 0, at every point on the ellipse we have

and

Using these facts we can easily sketch the ellipse. It is an oval curve inscribed in the rectangle bounded by the lines x = ±a, y = ±b.

Figure 5.5.3 shows a horizontal ellipse (where a > b) and a vertical ellipse (where a < b).

Figure 5.5.3

Example 1

Example 2