9.4. Ellipses http://www.ck12.org
3.
9 x^2 − 9 x+ 4 y^2 + 12 y+^94 =− 8
9 x^2 − 9 x+^94 + 4 y^2 + 12 y=− 8
9(
x^2 −x−^14)
+ 4 (y^2 + 3 y) =− 89(
x−^12) 2
+ 4
(
y^2 + 3 y+^94)
=− 8 + 4 ·^94
9
(
x−^12) 2
+ 4
(
y+^32) 2
= 1
(x− 1
2) 2
19 +
(y+ 3
2) 2
14 =^1
Practice
Find the vertices, foci, and eccentricity for each of the following ellipses.
1.(x− 41 )^2 +(y+ 165 )^2 = 1
2.(x+ 91 )^2 +(y+ 42 )^2 = 1
3.(x− 2 )^2 +(y− 41 )^2 = 1
Now sketch each of the following ellipses(note that they are the same as the ellipses in #1 - #3).
4.(x− 41 )^2 +(y+ 165 )^2 = 1
5.(x+ 91 )^2 +(y+ 42 )^2 = 1
6.(x− 2 )^2 +(y− 41 )^2 = 1
Put each of the following equations into graphing form.
7.x^2 + 2 x+ 4 y^2 + 56 y+ 197 = 16
8.x^2 − 8 x+ 9 y^2 + 18 y+ 25 = 9