1. Homework Log Thurs 4/21 Lesson 10 – 6 Learning Objective:
Stamping HW from Tues and maybe Wed
Homework Log
Today: Pg
In packet
Thurs
4/21
Lesson 10 – 6
Learning Objective:
To translate conics
Thurs Hw: Pg. 658
#7, 15 – 20, 27 – 31odd
Finish Wed’s HW (if u didn’t)

2. 4/21/16 Lesson 10 – 6 Translating Conics Day 1
Algebra II

3. Learning Objective To identify types of conics Circle Ellipse
Today: Pg
In packet
To identify types of conics
Circle
Ellipse
Hyperbola
Parabola

4. Identify the conic section, get into standard form, & graph
Today: Pg
In packet
1. 𝑥 2 +8𝑥+ 𝑦 2 =9
Circle 16
𝑥 2 +8𝑥 𝑦 2 =9+____ 16
𝑏 2 2 =
= 4 2
=16
(𝑥+4) 2 + 𝑦 2 =25
Circle
Center (-4, 0)
Radius = 5

5. Identify the conic section, get into standard form, & graph
Today: Pg
In packet
2. 𝑥+ 𝑦 2 −8𝑦+20=0
Parabola
𝑥= −𝑦 2 +8𝑦−20 16 16
𝑥= −(𝑦 2 −8𝑦+______)−20+_____
𝑏 2 2
= −
= −4 2
=16
𝑥= − 𝑦−4 2 −4
V(-4, 4)
Opens “x” left V

6. Identify the conic section, get into standard form, & graph
Today: Pg
In packet
3. 9 𝑥 2 + 𝑦 2 +54𝑥−6𝑦=−81
Ellipse
9 𝑥 2 +54𝑥+____ + 𝑦 2 −6𝑦+____ =−81+____ +____
9 𝑥 2 +6𝑥+____ + 𝑦 2 −6𝑦+____ =−81+____ +____ 9 9 81 9
𝑏 2 2 =
𝑏 2 2
= −
= 3 2 =9
= −3 2 =9
9(𝑥+3) 2 + (𝑦−3) 2 =9
(𝑥+3) (𝑦−3) 2 9 =1
Center (-3, 3)
Major Axis: y

7. Identify the conic section, get into standard form, & graph
Today: Pg
In packet
4. −9 𝑥 𝑦 2 −100𝑦−125=0
Hyperbola
−9 𝑥 𝑦 2 −100𝑦+____ =125+____
−9 𝑥 𝑦 2 −4𝑦+____ =125+____ 4
100
𝑏 2 2
= −
= −2 2 =4
−9 𝑥 (𝑦−2) 2 =225
- 𝑥 (𝑦−2) 2 9 =1
(𝑦−2) 2 9 − 𝑥 =1
Center (0, 2)
Opens: y

8. Identify the conic section, get into standard form, & graph
5. 9 𝑥 2 +4 𝑦 2 −54𝑥−8𝑦−59=0
Ellipse
9 𝑥 2 −54𝑥+____ + 4 𝑦 2 −8𝑦+____ =59+____ +____
9 𝑥 2 −6𝑥+____ +4 𝑦 2 −2𝑦+____ =59+____ +____ 9 1 81 4
𝑏 2 2
= −
𝑏 2 2
= −
= −3 2 =9
= −1 2 =1
9(𝑥−3) 2 +4 (𝑦−1) 2 =144
(𝑥−3) (𝑦−1) =1
Center (3, 1)
Major Axis: y

9. Identify the conic section, get into standard form, & graph
Today: Pg
In packet
Identify the conic section, get into standard form, & graph
6. −25 𝑥 2 + 𝑦 2 −100𝑥=125
Hyperbola
−25 𝑥 2 −100𝑥+____ + 𝑦 2 =125+____
−25 𝑥 2 +4𝑥+____ + 𝑦 2 =125+____ 4
−100
𝑏 2 2 =
= 2 2 =4
−25(𝑥+2) 2 + 𝑦 2 =25
𝑦 − (𝑥+2) 2 1 =1
− (𝑥+2) 𝑦 =1
Center (-2, 0)
Opens: y

10. Identify the conic section, get into standard form, & graph
7. 𝑥 2 +3 𝑦 2 +2𝑥−18𝑦−8=0
Ellipse
𝑥 2 +2𝑥+____ + 3 𝑦 2 −18𝑦+____ =8+____ +____
𝑥 2 +2𝑥+____ +3 𝑦 2 −6𝑦+____ =8+____ +____ 1 9 1 27
𝑏 2 2 =
𝑏 2 2
= −
= 1 2 =1
= −3 2 =9
(𝑥+1) 2 +3 (𝑦−3) 2 =36
(𝑥+1) (𝑦−3) =1
Center (-1, 3)
Major Axis: x

11. Identify the conic section, get into standard form, & graph
8. 𝑥 2 + 𝑦 2 +2𝑥+4𝑦=20
Circle
𝑥 2 +2𝑥+____ + 𝑦 2 +4𝑦+____ =20+____ +____
𝑥 2 +2𝑥+____ + 𝑦 2 +4𝑦+____ =20+____ +____ 1 4 1 4
𝑏 2 2 =
𝑏 2 2 =
= 1 2 =1
= 2 2 =4
(𝑥+1) 2 + (𝑦+2) 2 =25
Center (-1, -2)
Radius: 5

12. Identify the conic section, get into standard form, & graph
Parabola
y= 2 𝑥 2 +8𝑥+____ +1+____
y=2 𝑥 2 +4𝑥+____ +1+____ 4 -8
𝑏 2 2 =
= 2 2 =4
y=2 (𝑥+2) 2 −7
Vertex (-2, -7)
Opens “y” up

13. Identify the conic section, get into standard form, & graph
10. −4 𝑥 2 + 𝑦 2 −8𝑥−6𝑦=95
Hyperbola
−4 𝑥 2 −8𝑥+____ + 𝑦 2 −6𝑦+____ =95+____ +____
Factor
−4 𝑥 2 +2𝑥+____ + 𝑦 2 −6𝑦+____ =95+____ +____ 1 9 −4 9
𝑏 2 2 =
𝑏 2 2
= −
= 1 2 =1
= −3 2 =9
−4(𝑥+1) 2 + (𝑦−3) 2 =100
− (𝑥+1) (𝑦−3) =1
(𝑦−3) − (𝑥+1) =1
Center (-1, 3)
Opens: y