CK-12-Pre-Calculus Concepts

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

x^2 − 2 x+ 1 +(y− 2 )^2 =^94 (x^2 − 10 x+ 25 )

x^2 − 2 x+ 1 −^94 x^2 +^904 x−^2254 +(y− 2 )^2 = 0

−^54 x^2 +^924 x+(y− 2 )^2 =^2214

− 5 x^2 + 92 x+ 4 (y− 2 )^2 = 221

− 5

(

x^2 −^925 x

)

+ 4 (y− 2 )^2 = 221

− 5

(

x^2 −^925 x+^92

2

102

)

+ 4 (y− 2 )^2 = 221 −^21165

− 5

(

x−^9210

) 2

+ 4 (y− 2 )^2 =−^10115

(

x−^9210

) 2

−(y− 2 )^2 =^1011100

(x− 92

10

) 2

( 1011

100

) −(y−^2 )

2

( 1011

100

) = 1

Concept Problem Revisited
The best strategy to remember which direction the hyperbola opens is often the simplest. Consider the hyperbola
x^2 −y^2 =1. This hyperbola opens side to side becausexcan clearly never be equal to zero. This is a basic case that
shows that when the negative is with theyvalue then the hyperbola opens up side to side.

Vocabulary

Eccentricityis the ratio between the length of the focal radius and the length of the semi transverse axis. For
hyperbolas, the eccentricity is greater than one.
Ahyperbolais the collection of points that share a constant difference between the distances between two focus
points.

Guided Practice

1. Completely identify the components of the following conic.
   9 x^2 − 16 y^2 − 18 x+ 96 y+ 9 = 0


2. Given the following graph, estimate the equation of the conic.