http://www.ck12.org Chapter 9. Conics
When graphing, the constantsaandbenable you to draw a rectangle around the center. The transverse axis travels
from vertex to vertex and has length 2a. The conjugate axis travels perpendicular to the transverse axis through the
center and has length 2b. The foci lie beyond the vertices so the eccentricity, which is measured ase=ca, is larger
than 1 for all hyperbolas. Hyperbolas also have two directrix lines that areac^2 away from the center (not shown on
the image).
The focal radius isa^2 +b^2 =c^2.
Example A
Put the following hyperbola into graphing form and sketch it.
9 x^2 − 4 y^2 + 36 x− 8 y− 4 = 0
Solution:
9 (x^2 + 4 x)− 4 (y^2 + 2 y) = 4
9 (x^2 + 4 x+ 4 )− 4 (y^2 + 2 y+ 1 ) = 4 + 36 − 4
9 (x+ 2 )^2 − 4 (y+ 1 )^2 = 36
(x+ 2 )^2
4 −(y+ 1 )^2
9 =^1