Homework Log Thurs 4/21 Lesson 10 – 6 Learning Objective: Stamping HW from Tues and maybe Wed Homework Log Today: Pg. 21-24 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)

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

Learning Objective To identify types of conics Circle Ellipse Today: Pg. 21-24 In packet To identify types of conics Circle Ellipse Hyperbola Parabola

Identify the conic section, get into standard form, & graph Today: Pg. 21-24 In packet 1. 𝑥 2 +8𝑥+ 𝑦 2 =9 Circle 16 𝑥 2 +8𝑥 + + 𝑦 2 =9+____ 16 𝑏 2 2 = 8 2 2 = 4 2 =16 (𝑥+4) 2 + 𝑦 2 =25 Circle Center (-4, 0) Radius = 5

Identify the conic section, get into standard form, & graph Today: Pg. 21-24 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 = −8 2 2 = −4 2 =16 𝑥= − 𝑦−4 2 −4 V(-4, 4) Opens “x” left V

Identify the conic section, get into standard form, & graph Today: Pg. 21-24 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 = 6 2 2 𝑏 2 2 = −6 2 2 = 3 2 =9 = −3 2 =9 9(𝑥+3) 2 + (𝑦−3) 2 =9 (𝑥+3) 2 1 + (𝑦−3) 2 9 =1 Center (-3, 3) Major Axis: y

Identify the conic section, get into standard form, & graph Today: Pg. 21-24 In packet 4. −9 𝑥 2 +25 𝑦 2 −100𝑦−125=0 Hyperbola −9 𝑥 2 + 25 𝑦 2 −100𝑦+____ =125+____ −9 𝑥 2 +25 𝑦 2 −4𝑦+____ =125+____ 4 100 𝑏 2 2 = −4 2 2 = −2 2 =4 −9 𝑥 2 +25 (𝑦−2) 2 =225 - 𝑥 2 25 + (𝑦−2) 2 9 =1 (𝑦−2) 2 9 − 𝑥 2 25 =1 Center (0, 2) Opens: y

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 = −6 2 2 𝑏 2 2 = −2 2 2 = −3 2 =9 = −1 2 =1 9(𝑥−3) 2 +4 (𝑦−1) 2 =144 (𝑥−3) 2 16 + (𝑦−1) 2 36 =1 Center (3, 1) Major Axis: y

Identify the conic section, get into standard form, & graph Today: Pg. 21-24 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 = 4 2 2 = 2 2 =4 −25(𝑥+2) 2 + 𝑦 2 =25 𝑦 2 25 − (𝑥+2) 2 1 =1 − (𝑥+2) 2 1 + 𝑦 2 25 =1 Center (-2, 0) Opens: y

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 = 2 2 2 𝑏 2 2 = −6 2 2 = 1 2 =1 = −3 2 =9 (𝑥+1) 2 +3 (𝑦−3) 2 =36 (𝑥+1) 2 36 + (𝑦−3) 2 12 =1 Center (-1, 3) Major Axis: x

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 = 2 2 2 𝑏 2 2 = 4 2 2 = 1 2 =1 = 2 2 =4 (𝑥+1) 2 + (𝑦+2) 2 =25 Center (-1, -2) Radius: 5

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 = 4 2 2 = 2 2 =4 y=2 (𝑥+2) 2 −7 Vertex (-2, -7) Opens “y” up

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 = 2 2 2 𝑏 2 2 = −6 2 2 = 1 2 =1 = −3 2 =9 −4(𝑥+1) 2 + (𝑦−3) 2 =100 − (𝑥+1) 2 25 + (𝑦−3) 2 100 =1 (𝑦−3) 2 100 − (𝑥+1) 2 25 =1 Center (-1, 3) Opens: y