Section 10.2 Ellipses

Objective By following instructions students will be able to: Write equations of ellipses in standard form. Use properties of ellipses to model and solve real-life problems. Find eccentricities of ellipses.

Ellipses in Real life

Def: An ellipse is the set of all points P in a plane such that the sum of the distances between P and two fixed points, called the foci, is a constant. If the ellipses are translated, then the equations are: x y x y

EXAMPLE 1: Sketch the ellipse given by . Identify the vertices, Co-vertices, and foci of the ellipse.

U-TRY #1 Graph the equation. Identify the vertices, co-vertices, and foci of the ellipses. A) B) C)

EXAMPLE 2: Find the standard form of the equation of the ellipse having foci at (0,1) and (4,1), and a major axis of length 6.

EXAMPLE 3: Identify the conic section. Next, write the equation in standard form and sketch its graph. Label all of its parts.

EXAMPLE 4: Identify the conic section. Next, write the equation in standard form and sketch its graph. Label all of its parts.

U-TRY #2 Classify the conic section and write its equation in standard form. A) B) C) D)

EXAMPLE 5: The moon travels about the earth in an elliptical orbit with the earth at one focus, as shown in the figure. The major and minor axes of the orbit have lengths of 768,806 kilometers and 767,746 kilometers, respectively. Find the greatest and least distances (the apogee and perigee) from the earth’s center to the moon’s center.

Revisit Objective Did we… Write equation of ellipses in standard form? Use properties of ellipses to model and solve real-life problems? Find eccentricities of ellipses?

Homework Pg 710 #s1-45 ODD