http://www.ck12.org Chapter 9. Conics
Practice
- What are the three degenerate conics?
Change each equation into graphing form and state what type of conic or degenerate conic it is.
2.x^2 − 6 x− 9 y^2 − 54 y− 72 = 0 - 4x^2 + 16 x− 9 y^2 + 18 y− 29 = 0
- 9x^2 + 36 x+ 4 y^2 − 24 y+ 72 = 0
- 9x^2 + 36 x+ 4 y^2 − 24 y+ 36 = 0
- 0x^2 + 5 x+ 0 y^2 − 2 y+ 1 = 0
7.x^2 + 4 x−y+ 8 = 0
8.x^2 − 2 x+y^2 − 6 y+ 6 = 0
9.x^2 − 2 x− 4 y^2 + 24 y− 35 = 0
10.x^2 − 2 x+ 4 y^2 − 24 y+ 33 = 0
Sketch each conic or degenerate conic.
11.(x+ 42 )^2 +(y− 93 )^2 = 0
12.(x− 93 )^2 +(y+ 163 )^2 = 1
13.(x+ 92 )^2 −(y− 41 )^2 = 1
14.(x− 93 )^2 −(y+ 43 )^2 = 0
- 3x+ 4 y= 12
You learned that a conic section is the family of shapes that are formed by the different ways a flat plane intersects a
two sided cone in three dimensional space. Parabolas, circles, ellipses and hyperbolas each have their own graphing
form of equations that helped you identify information about them like the focus and the directrix.