Chapter 9:Quadratic Relations

and Systems

Section 9-3: Ellipses

Objectives:Given the equation of an ellipse:

Sketch the graph

Calculate the focal radii and plot the foci

Check the sketch by computer graphics

EllipseAn ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve.

Graph of an Ellipse

X-Radius and Y-RadiusIf an ellipse has its major and minor axes parallel to the coordinate axes, then:

The x-radius is the distance from the center to the ellipse in the x-direction.

The y-radius is the distance from the center to the ellipse in the y-direction

Equation for an Ellipse

22

1x y

x h y k

r r

Example 1:Sketch the graph of:

2 225 9 200 18 184 0x y x y

HOMEWORK

p. 476 #1-15 odd