http://www.ck12.org Chapter 9. Conics
f. Hyperbola
2.
6 y^2 − 36 y+ 4
6 (y^2 − 6 y+ )+ 4
6 (y^2 − 6 y+ 9 )+ 4 − 54
6 (y− 3 )^2 − 50− 3 x^2 − 24 x+ 4 y^2 − 32 y= 8
− 3 (x^2 + 8 x+ )+ 4 (y^2 − 8 y+ ) = 8
− 3 (x^2 + 8 x+ 16 )+ 4 (y^2 − 8 y+ 16 ) = 8 − 48 + 64
− 3 (x+ 4 )^2 + 4 (y− 4 )^2 = 24Practice
Identify the type of conic in each of the following relations.
- 3x^2 + 4 y^2 = 12
2.x^2 +y^2 = 9
3.x 42 +y 92 = 1
4.y^2 +x= 11
5.x^2 + 2 x−y^2 + 6 y= 15
6.x^2 =y− 1
Complete the square forxand/oryin each of the following expressions.
7.x^2 + 4 x
8.y^2 − 8 y
- 3x^2 + 6 x+ 4
- 3y^2 + 9 y+ 15
- 2x^2 − 12 x+ 1
Complete the square forxand/oryin each of the following equations. - 4x^2 − 16 x+y^2 + 2 y=− 1
- 9x^2 − 54 x+y^2 − 2 y=− 81
- 3x^2 − 6 x− 4 y^2 = 9
15.y=x^2 + 4 x+ 1