1. Homework Log Wed 4/27 Lesson Rev Learning Objective:
To remember everything on conics
Hw: STUDY!
Stamp log due Thurs.

2. 4/27/16 Chapter 10 Conics
Algebra II

3. Learning Objective
To graph conics
To write equations of conics

4. Write an equation of a parabola with the given information
1. Vertex (1, 4), Focus (1, -2)
V(h, k) V
c = -6
𝑦= 1 4𝑐 (𝑥−ℎ) 2 +𝑘 F
𝑦= 1 4(−6) (𝑥−1) 2 +4
𝑦=− (𝑥−1)

5. Write an equation of a parabola with the given information
2. Focus (2, 3), Directrix y = -1 F
𝑦= 1 4𝑐 (𝑥−ℎ) 2 +𝑘
c = 2 D
𝑦= 1 4(2) (𝑥−2) 2 +1
V(2, 1)
𝑦= 𝑥−
V(h, k)

6. Write an equation of a parabola with the given information
3. V(0, -3), Directrix x = 1.25
c = -1.25
V(h, k)
𝑥= 1 4𝑐 (𝑦−𝑘) 2 +ℎ V
𝑥= 1 4(−1.25) (𝑦+3) 2 +0 D
𝑥=− 1 5 (𝑦+3) 2

7. Get into vertex form. Find vertex, focus, and directrix. Sketch a graph.
4. y=2 𝑥 2 +8𝑥+11
V(-2, 3)
𝑦=2 𝑥 2 +4𝑥+_____ +11+____ 4 −8
D: y = 2 7 8
𝑏 2 2 =
= 2 2 =4
𝑦=2 (𝑥+2) 2 +3 F D V
𝑦= 1 4𝑐 (𝑥−ℎ) 2 +𝑘
2 1 = 1 4𝑐
8𝑐=1
𝑐= 1 8
Opens “y” up

8. D
Get into vertex form if it isn’t already. Find vertex, focus, and directrix. Sketch a graph.
5. 𝑥=− 𝑦
𝑥= 1 4𝑐 (𝑦−𝑘) 2 +ℎ
V(5, -2)
− 1 8 = 1 4𝑐
F(3, -2) V F
4𝑐=−8
𝑐=−2
D: x = 7
Opens “x” left

9. Write an equation of a circle with the given information
6. Center (-4, 0), radius 9
(𝑥−ℎ) 2 + (𝑦−𝑘) 2 = 𝑟 2
(𝑥−(−4)) 2 + (𝑦−0) 2 = 9 2
(𝑥+4) 2 + 𝑦 2 =81

10. Write an equation of a circle with the given information
(h, k)
7. Center (-3, 2),
point on the circle (1, 5)
𝑟= (1−(−3)) 2 + (5−2) 2
𝑟= (4) 2 + (3) 2
𝑟=5
(𝑥−ℎ) 2 + (𝑦−𝑘) 2 = 𝑟 2
(𝑥−(−3)) 2 + (𝑦−2) 2 = 5 2
(𝑥+3) 2 + (𝑦−2) 2 =25

11. Write an equation of a circle with the given information
8. Endpoints of a diameter (2, 1) & (-2, 3)
𝑟= 1 2 𝑑
𝑟= (3−1) 2 + (−2−2) 2
𝑟= (2) 2 + (−4) 2 = =
= 5
𝐶= 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2
= −2+2 2 , 3+1 2
center=(0, 2)
(h, k)
(𝑥−ℎ) 2 + (𝑦−𝑘) 2 = 𝑟 2
𝑥− 𝑦−2 2 =
𝑥 2 +( 𝑦−2) 2 =5

12. Find the center & radius of the circle & graph
9. 𝑥 2 + 𝑦 2 −2𝑥+8𝑦=9
( 𝑥 2 −2𝑥+____)+( 𝑦 2 +8𝑦+____)=9+____ +____ 1 16 1 16
𝑏 2 2
= −
= −1 2 =1
𝑏 2 2 =
= 4 2
= 16
(𝑥−1) 2 +( 𝑦+4) 2 =26
Center: (1, -4)
Radius: 26
≈5.1

13. Find the center, vertices, co-vertices & foci
Find parts
Sketch Graph
Look at Graph
10. 𝑥 𝑦 =1
Major Axis: y
a = 5
b = 2
Center (0, 0)
V(0,±5)
CV(±2,0)
F(0,± 21 )
𝑐 2 = 𝑎 2 − 𝑏 2
𝑐 2 = 5 2 − 2 2
𝑐 2 =21
c= 21

14. Write an equation of an ellipse with the given information
11. Co-vertices (0, ±3), major axis length 8
Major Axis: x
Sketch Graph
Find parts (look at graph)
a = 4
b = 3
b = 3
(𝑥−ℎ) 2 𝑎 (𝑦−𝑘) 2 𝑏 2 =1
Plug in
(𝑥−0) (𝑦−0) =1
a = 4
𝑥 𝑦 2 9 =1

15. Find the center, vertices, co-vertices & foci
12. 𝑥 2 9 − 𝑦 =1
Opens: x
a = 3
b = 5
Center (0, 0)
V(±3, 0)
F(± 34 ,0)
Asym: y=± 5 3 𝑥
𝑐 2 = 𝑎 2 + 𝑏 2
𝑐 2 =
𝑐 2 =34
c= 34

16. Write an equation of a hyperbola with the given information
13. Foci (0, ±4), Vertices (0, ±3)
Center is between vertices
Center (0, 0)
Opens: y
c = 4
a = 3
c = 4
𝑐 2 = 𝑎 2 + 𝑏 2
a = 3
(𝑦−𝑘) 2 𝑎 2 − (𝑥−ℎ) 2 𝑏 2 =1
4 2 = 𝑏 2
(𝑦−0) 2 (3) 2 − (𝑥−0) =1
b= 7
𝑦 2 9 − 𝑥 2 7 =1

17. Identify the conic section, get into standard form, & graph
14. 4 𝑥 2 − 𝑦 2 −16𝑥−2𝑦−1=0
Hyperbola
(4 𝑥 2 −16𝑥+____)+ − 𝑦 2 −2𝑦+____ =1+____+____
4 𝑥 2 −4𝑥+____ − 𝑦 2 +2𝑦+____ =1+____+____ 4 1 16 -1
𝑏 2 2
= −
𝑏 2 2 =
= −2 2 =4
= 1 2 =1
4 (𝑥−2) 2 − (𝑦+1) 2 =16
(𝑥−2) 2 4 − (𝑦+1) =1
Center (2, -1)
Opens: x

18. #14 Cont’d (𝑥−2) 2 4 − (𝑦+1) 2 16 =1 𝑐 2 = 𝑎 2 + 𝑏 2 𝑐 2 = 2 2 + 4 2
Opens: x
a = 2
b =4
(look at graph)
Center (2, -1)
V(0, -1) (4, -1)
F(2±2 5 ,−1)
𝑐 2 = 𝑎 2 + 𝑏 2
𝑐 2 =
c=2 5
𝑐 2 =20
Add along x

19. Identify the conic section, get into standard form, & graph
15. 𝑥 2 +4 𝑦 2 +6𝑥−32𝑦+57=0
Ellipse
𝑥 2 +6𝑥+____ + 4𝑦 2 −32𝑦+____ =−57+____+____
𝑥 2 +6𝑥+____ +4 𝑦 2 −8𝑦+____ =−57+____+____ 9 16 9 64
𝑏 2 2 =
𝑏 2 2
= −
= 3 2 =9
= −4 2
=16
(𝑥+3) 2 +4( 𝑦−4) 2 =16
(𝑥+3) ( 𝑦−4) 2 4 =1
Center (-3, 4)
Major Axis: x

20. #15 Cont’d (𝑥+3) ( 𝑦−4) 2 4 =1
Major Axis: x
a = 4
b = 2
(look at graph)
Center (-3, 4)
V(1, 4) (-7, 4)
CV (-3, 2) (-3, 6)
F(-3±2 3 , 4)
𝑐 2 = 𝑎 2 − 𝑏 2
𝑐 2 = 4 2 − 2 2
c=2 3
𝑐 2 =12
Add along x