CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 9. Conics

Eccentricity is the ratio of the focal radius to the semi major axis: e=ca.

Vocabulary

Thesemi-major axisis the distance from the center of the ellipse to the furthest point on the ellipse. The lettera
represents the length of the semi-major axis.
Themajor axisis the longest distance from end to end of an ellipse. This distance is twice that of the semi-major
axis.
Thesemi-minor axisis the distance from the center to the edge of the ellipse on the axis that is perpendicular to the
semi-major axis. The letterbrepresents the length of the semi-minor axis.
Anellipseis the collection of points whose sum of distances from two foci is constant.
Thefociin an ellipse are the two points that the ellipse curves around.
Eccentricityis a measure of how oval or how circular the shape is. It is the ratio of the focal radius to the semi
major axis:e=ca.

Guided Practice

1. Find the vertices (endpoints of the major axis), foci and eccentricity of the following ellipse.
   (x− 42 )^2 +(y+ 161 )^2 = 1


2. Sketch the following ellipse.

(x− 3 )^2 +(y− 91 )^2 = 1

3. Put the following conic into graphing form.
   9 x^2 − 9 x+ 4 y^2 + 12 y+^94 =− 8
   Answers:


4. The center of the ellipse is at (2, -1). The major axis is vertical which means the semi major axis isa=4. The
   vertices are (2, 3) and (2, -5).

162 − 42 =c^2

4

√

15 =

√

240 =c

Thus the foci are( 2 ,− 1 + 4

√

15 )and( 2 ,− 1 − 4

√

15 )

2.