1. Chapter 10
Conic Sections

2. Chapter Sections 10.1 – The Parabola and the Circle 10.2 – The Ellipse
10.3 – The Hyperbola
10.4 – Nonlinear Systems of Equations and Their Applications
Chapter 1 Outline

3. § 10.2
The Ellipse

4. Graph Ellipses Ellipse
An ellipse is a set of point in a plane, the sum of whose distances from two fixed points is a constant. The two fixed points are called the foci (each is a focus) of the ellipse.
F1 and F2 represent the two foci of an ellipse

5. Graph Ellipses Ellipse with Its Center at the Origin
The standard form of an ellipse with its center at the origin is
Where (a, 0) and (-a, 0) are the x-intercepts and (0, b) and (0, -b) are the y-intercepts.

6. Graph Ellipses Observe that:
The x-intercepts are obtained from the constant in the denominator of the x-term.
The y-intercepts are obtained from the constant in the denominator of the y-term.
If a2 > b2, the major axis is along the x-axis.
If b2 > a2, the major axis is along the y-axis.

7. Graph Ellipses Example Graph . We can rewrite the equation as
Thus, a = 3, and x-intercepts are (3, 0) and (-3, 0). Since b = 2, the y-intercepts are (0, 2) and (0, -2). The graph is shown to the right.

8. Graph Ellipses with Centers at (h, k)
Ellipse with Its Center at (h, k)
In the formula, h shifts the graph left or right from the origin and k shifts the graph up or down from the origin.

9. Graph Ellipses with Centers at (h, k)
This is the graph of
translated so that its center is at (2, -3). Note that a = 5 and b = 4. The graph is shown to the right.